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Physics Problems for Moving Charges and Magnetism
A premium problem bank with assignment-inspired numerical problems, NCERT-style concept flow, clean redrawn SVG diagrams, detailed solutions, direction rules, formula sheets, NEET/JEE traps and board-answer guidance.
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Chapter Roadmap
1. Magnetic Force on Moving Charge
Formula, diagram, direction rule, solved problem and exam traps are covered in this section.
2. Motion of Charged Particle in Magnetic Field
Formula, diagram, direction rule, solved problem and exam traps are covered in this section.
3. Circular Motion and Helical Motion
Formula, diagram, direction rule, solved problem and exam traps are covered in this section.
4. Biot-Savart Law
Formula, diagram, direction rule, solved problem and exam traps are covered in this section.
5. Magnetic Field due to Straight Wire
Formula, diagram, direction rule, solved problem and exam traps are covered in this section.
6. Magnetic Field due to Circular Coil
Formula, diagram, direction rule, solved problem and exam traps are covered in this section.
7. Magnetic Field on Axis of Circular Loop
Formula, diagram, direction rule, solved problem and exam traps are covered in this section.
8. Ampere Circuital Law
Formula, diagram, direction rule, solved problem and exam traps are covered in this section.
9. Solenoid and Toroid
Formula, diagram, direction rule, solved problem and exam traps are covered in this section.
10. Force Between Parallel Current Carrying Conductors
Formula, diagram, direction rule, solved problem and exam traps are covered in this section.
11. Torque on Current Loop
Formula, diagram, direction rule, solved problem and exam traps are covered in this section.
12. Moving Coil Galvanometer
Formula, diagram, direction rule, solved problem and exam traps are covered in this section.
13. Mixed Advanced Problems
Formula, diagram, direction rule, solved problem and exam traps are covered in this section.
One-Page Formula Sheet
Lorentz Force
F = q(v × B), |F| = qvB sinθForce on Conductor
F = BIL sinθCircular Radius
r = mv/qBTime Period
T = 2πm/qBFrequency
f = qB/2πmHelical Pitch
p = v cosθ × TBiot-Savart Law
dB = (μ₀/4π) I dl sinθ/r²Straight Wire
B = μ₀I/2πrCircular Loop Centre
B = μ₀NI/2RCircular Loop Axis
B = μ₀NIR²/[2(R²+x²)³ᐟ²]Ampere Law
∮B·dl = μ₀I_enclosedSolenoid
B = μ₀nIToroid
B = μ₀NI/2πrParallel Currents
F/L = μ₀I₁I₂/2πdTorque on Loop
τ = NIAB sinθGalvanometer
NBIA = kθ, I = kθ/NBAAssignment-Inspired Problems with Clean SVG Diagrams
These problems are redrawn and rewritten in original educational language from the uploaded assignment pattern. Diagrams are clean SVGs, not screenshots.
Problem 0. Small current element on y-axisStraight Conductor
Assignment-inspired redrawn SVG; NCERT Class 12 Moving Charges and Magnetism used as concept reference.
A current element dl = dx î, where dx = 1 cm, is placed at the origin and carries current I = 10 A. Find magnetic field at a point on the y-axis at distance 0.5 m.
Given: I = 10 A, dl = 0.01 m, r = 0.5 m, angle = 90°.
Required: Magnetic field at P.
Formula used: dB = (μ₀/4π) I dl sinθ/r².
- Identify concept: Straight Conductor.
- Substitute and solve: Substitute μ₀/4π = 10⁻⁷, I = 10, dl = 10⁻² and r² = 0.25. dB = 10⁻⁷ × 10 × 10⁻² / 0.25 = 4 × 10⁻⁸ T. Direction is obtained by dl × r, along +k̂.
- Final answer: B = 4 × 10⁻⁸ k̂ T.
Common mistake: Ignoring direction, sign or vector addition. Always apply right-hand rule before adding magnitudes.
Problem 1. Two mutually perpendicular long wiresPerpendicular Conductors
Assignment-inspired redrawn SVG; NCERT Class 12 Moving Charges and Magnetism used as concept reference.
Two long insulating wires are mutually perpendicular. Currents 2 A and 1.5 A flow as shown. Point P is 4 cm from the vertical wire and 3 cm from the horizontal wire. Find net magnetic field at P.
Given: I₁ = 2 A, r₁ = 4 cm; I₂ = 1.5 A, r₂ = 3 cm.
Required: Net magnetic field at P.
Formula used: B = μ₀I/2πr.
- Identify concept: Perpendicular Conductors.
- Substitute and solve: For the vertical wire, B₁ = 2×10⁻⁷ × 2/0.04 = 1×10⁻⁵ T. For the horizontal wire, B₂ = 2×10⁻⁷ × 1.5/0.03 = 1×10⁻⁵ T. The directions are same by right-hand rule, so they add.
- Final answer: B = 2 × 10⁻⁵ T.
Common mistake: Ignoring direction, sign or vector addition. Always apply right-hand rule before adding magnitudes.
Problem 2. Magnetic field at centre of rectangular loopRectangular Loop
Assignment-inspired redrawn SVG; NCERT Class 12 Moving Charges and Magnetism used as concept reference.
A rectangular loop of sides a and b carries current I. Find magnetic field at its centre O.
Given: Current I, length a, breadth b.
Required: B at centre O.
Formula used: B for finite straight wire: B = (μ₀I/4πr)(sinα + sinβ).
- Identify concept: Rectangular Loop.
- Substitute and solve: Find contribution of each side using the finite-wire formula. Opposite sides give equal contributions and all directions are same at the centre. Adding four side contributions gives the compact rectangular-loop result.
- Final answer: B = [2μ₀I√(a²+b²)]/(πab), perpendicular to the plane.
Common mistake: Ignoring direction, sign or vector addition. Always apply right-hand rule before adding magnitudes.
Problem 3. Two semi-infinite wires with equal currentAngled Wires
Assignment-inspired redrawn SVG; NCERT Class 12 Moving Charges and Magnetism used as concept reference.
Two wires CO and OA carry equal currents I and extend to infinity. If ∠AOC = θ, find B at point P on the angle bisector at distance r from O.
Given: Equal current I, angle θ, OP = r on angle bisector.
Required: Magnetic field at P.
Formula used: Finite/semi-infinite wire formula and perpendicular distance to each arm.
- Identify concept: Angled Wires.
- Substitute and solve: Use the finite straight conductor expression for both semi-infinite arms. The perpendicular distance from P to either arm is r sin(θ/2). The angular factor gives 1 + cos(θ/2) for each branch. Add both equal contributions.
- Final answer: B = (μ₀/4π) [2I/r] [(1 + cos(θ/2))/sin(θ/2)].
Common mistake: Ignoring direction, sign or vector addition. Always apply right-hand rule before adding magnitudes.
Problem 4. Three parallel wires at x = 1 m, 2 m and 4 mParallel Wires
Assignment-inspired redrawn SVG; NCERT Class 12 Moving Charges and Magnetism used as concept reference.
Equal currents I = 1 A flow through long wires parallel to the y-axis at x = 1 m, 2 m and 4 m. Directions are up, down and up respectively. Find magnetic field at origin.
Given: I = 1 A, distances 1 m, 2 m, 4 m.
Required: B at O.
Formula used: B = μ₀I/2πr, direction by right-hand rule.
- Identify concept: Parallel Wires.
- Substitute and solve: At O, add signed fields due to three wires. The wire at x = 1 m contributes one way, x = 2 m contributes the same way because current is reversed, and x = 4 m contributes opposite. Net coefficient is 1 + 1/2 - 1/4 = 5/4 times 2×10⁻⁷.
- Final answer: B = 2.5 × 10⁻⁷ T with direction fixed by right-hand rule.
Common mistake: Ignoring direction, sign or vector addition. Always apply right-hand rule before adding magnitudes.
Problem 5. Circular coil with N turnsCircular Coil
Assignment-inspired redrawn SVG; NCERT Class 12 Moving Charges and Magnetism used as concept reference.
A circular coil of N turns, radius R, carries current I. Find B at centre and at axial distance x.
Given: N, I, R and x.
Required: B at O and P.
Formula used: Bcentre = μ₀NI/2R, Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²].
- Identify concept: Circular Coil.
- Substitute and solve: Use Biot-Savart law. At the centre, all elements contribute same direction. At axial point, transverse components cancel and axial components add.
- Final answer: Bcentre = μ₀NI/2R; Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²].
Common mistake: Ignoring direction, sign or vector addition. Always apply right-hand rule before adding magnitudes.
Problem 6. Field at centre of semicircular arcSemicircular Arc
Assignment-inspired redrawn SVG; NCERT Class 12 Moving Charges and Magnetism used as concept reference.
A current carrying wire is bent into a semicircular arc of radius R. Find magnetic field at the centre.
Given: Current I, radius R, angle π rad.
Required: B at centre.
Formula used: B_arc = μ₀Iθ/4πR.
- Identify concept: Semicircular Arc.
- Substitute and solve: Straight radial joining parts give zero at the centre if the point lies along their extension. For a semicircle θ = π, so B = μ₀Iπ/4πR.
- Final answer: B = μ₀I/4R, direction by right-hand rule.
Common mistake: Ignoring direction, sign or vector addition. Always apply right-hand rule before adding magnitudes.
Problem 7. Current density varying as J = kr²Ampere Law
Assignment-inspired redrawn SVG; NCERT Class 12 Moving Charges and Magnetism used as concept reference.
In a cylindrical conductor of radius a, current density varies as J = kr². Find magnetic field at distance r from the axis for r < a and r > a.
Given: J = kr², conductor radius a.
Required: B inside and outside.
Formula used: ∮B·dl = μ₀I_enclosed.
- Identify concept: Ampere Law.
- Substitute and solve: For r < a, I_enclosed = ∫₀ʳ kρ²(2πρ dρ) = πkr⁴/2. Therefore B(2πr)=μ₀πkr⁴/2. For outside, use total current at r=a.
- Final answer: Inside: B = μ₀kr³/4. Outside: B = μ₀ka⁴/(4r).
Common mistake: Ignoring direction, sign or vector addition. Always apply right-hand rule before adding magnitudes.
Problem 8. Field of a long solenoidSolenoid
Assignment-inspired redrawn SVG; NCERT Class 12 Moving Charges and Magnetism used as concept reference.
A long solenoid has length l, total turns N and current I. Find magnetic field inside and near one end.
Given: N turns, length l, current I.
Required: B inside and at end.
Formula used: B_inside = μ₀nI where n = N/l.
- Identify concept: Solenoid.
- Substitute and solve: Apply Ampere law to a rectangular loop partly inside and partly outside. Outside field is negligible for a long solenoid. At one end, field is approximately half of central value.
- Final answer: Bcentre = μ₀(N/l)I; Bend ≈ μ₀(N/l)I/2.
Common mistake: Ignoring direction, sign or vector addition. Always apply right-hand rule before adding magnitudes.
Problem 9. Force between same-direction currentsParallel Conductors
Assignment-inspired redrawn SVG; NCERT Class 12 Moving Charges and Magnetism used as concept reference.
Two long parallel wires separated by distance d carry currents I₁ and I₂ in the same direction. Find force per unit length and state nature.
Given: I₁, I₂, separation d.
Required: F/L and nature.
Formula used: B₁ at wire 2 = μ₀I₁/2πd; F₂/L = I₂B₁.
- Identify concept: Parallel Conductors.
- Substitute and solve: Field produced by wire 1 at wire 2 acts perpendicular to current in wire 2. Applying Fleming left hand rule or vector product gives attraction for same directions.
- Final answer: F/L = μ₀I₁I₂/(2πd), attractive.
Common mistake: Ignoring direction, sign or vector addition. Always apply right-hand rule before adding magnitudes.
Problem 10. Current loop in uniform magnetic fieldTorque on Loop
Assignment-inspired redrawn SVG; NCERT Class 12 Moving Charges and Magnetism used as concept reference.
A rectangular coil of N turns and area A carries current I in magnetic field B. Find torque.
Given: N, I, A, B, angle θ between magnetic moment and B.
Required: Torque.
Formula used: τ = mB sinθ, m = NIA.
- Identify concept: Torque on Loop.
- Substitute and solve: Forces on opposite sides form a couple. Net force is zero but torque is not zero when the magnetic moment is not parallel to B.
- Final answer: τ = NIAB sinθ.
Common mistake: Ignoring direction, sign or vector addition. Always apply right-hand rule before adding magnitudes.
Problem 11. Torque balance in MCGMoving Coil Galvanometer
Assignment-inspired redrawn SVG; NCERT Class 12 Moving Charges and Magnetism used as concept reference.
A moving coil galvanometer has N turns, area A, field B and torsional constant k. Derive current-deflection relation.
Given: N, A, B, k and deflection θ.
Required: I in terms of θ.
Formula used: Deflecting torque = NBIA, restoring torque = kθ.
- Identify concept: Moving Coil Galvanometer.
- Substitute and solve: In radial field, magnetic torque is NBIA independent of angle. At equilibrium NBIA = kθ.
- Final answer: I = kθ/NBA; current sensitivity = NBA/k.
Common mistake: Ignoring direction, sign or vector addition. Always apply right-hand rule before adding magnitudes.
Concept Map and Direction Rule Summary
Right-hand thumb rule
Thumb shows current; curled fingers show magnetic field around a straight wire.
Dot and cross
Dot means out of page; cross means into page.
Magnetic force
Force is perpendicular to both velocity/current and magnetic field.
Same currents
Parallel currents in the same direction attract.
Opposite currents
Parallel currents in opposite directions repel.
Loop torque
Current loop behaves like magnetic dipole with m = NIA.
Exam-Oriented Question Bank
Every MCQ includes options, correct answer, explanation, shortcut and common trap.
CBSE Theory Questions
CBSE Subjective 1Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 2Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 3Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 4Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 5Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 6Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 7Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 8Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 9Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 10Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 11Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 12Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 13Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 14Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 15Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 16Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 17Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 18Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 19Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 20Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 21Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 22Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 23Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 24Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 25Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 26Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 27Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 28Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 29Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 30Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 31Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 32Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 33Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 34Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 35Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 36Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 37Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 38Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 39Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 40Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 41Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 42Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 43Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 44Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 45Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 46Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 47Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 48Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 49Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Subjective 50Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for CBSE.
CBSE Numerical Questions
CBSE Numerical Question 1A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
CBSE Numerical Question 2A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Board-Oriented
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
CBSE Numerical Question 3Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Board-Oriented
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Board-Oriented
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
CBSE Numerical Question 4For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Board-Oriented
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
CBSE Numerical Question 5In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
CBSE Numerical Question 6A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
CBSE Numerical Question 7The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
CBSE Numerical Question 8For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Board-Oriented
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
CBSE Numerical Question 9A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Board-Oriented
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
CBSE Numerical Question 10A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Board-Oriented
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
CBSE Numerical Question 11Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Board-Oriented
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Board-Oriented
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
CBSE Numerical Question 12For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Board-Oriented
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
CBSE Numerical Question 13In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Board-Oriented
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
CBSE Numerical Question 14A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
CBSE Numerical Question 15The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Board-Oriented
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
CBSE Numerical Question 16For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Circular Motion and Helical Motion
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Board-Oriented
Concept Tested: Circular Motion and Helical Motion
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
CBSE Numerical Question 17A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Biot-Savart Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Board-Oriented
Concept Tested: Biot-Savart Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
CBSE Numerical Question 18A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
CBSE Numerical Question 19Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
CBSE Numerical Question 20For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
CBSE Numerical Question 21In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Ampere Circuital Law
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Board-Oriented
Concept Tested: Ampere Circuital Law
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
CBSE Numerical Question 22A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Solenoid and Toroid
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Board-Oriented
Concept Tested: Solenoid and Toroid
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
CBSE Numerical Question 23The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Board-Oriented
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
CBSE Numerical Question 24For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Torque on Current Loop
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Board-Oriented
Concept Tested: Torque on Current Loop
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
CBSE Numerical Question 25A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Moving Coil Galvanometer
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Board-Oriented
Concept Tested: Moving Coil Galvanometer
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
CBSE Numerical Question 26A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Mixed Advanced Problems
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Board-Oriented
Concept Tested: Mixed Advanced Problems
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
CBSE Numerical Question 27Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
CBSE Numerical Question 28For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Board-Oriented
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
CBSE Numerical Question 29In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Circular Motion and Helical Motion
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Board-Oriented
Concept Tested: Circular Motion and Helical Motion
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
CBSE Numerical Question 30A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Biot-Savart Law
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Board-Oriented
Concept Tested: Biot-Savart Law
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
CBSE Numerical Question 31The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
CBSE Numerical Question 32For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
CBSE Numerical Question 33A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
CBSE Numerical Question 34A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Ampere Circuital Law
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Board-Oriented
Concept Tested: Ampere Circuital Law
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
CBSE Numerical Question 35Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Board-Oriented
Concept Tested: Solenoid and Toroid
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Board-Oriented
Concept Tested: Solenoid and Toroid
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
CBSE Numerical Question 36For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Board-Oriented
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
CBSE Numerical Question 37In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Torque on Current Loop
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Board-Oriented
Concept Tested: Torque on Current Loop
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
CBSE Numerical Question 38A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Moving Coil Galvanometer
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Board-Oriented
Concept Tested: Moving Coil Galvanometer
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
CBSE Numerical Question 39The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Mixed Advanced Problems
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Board-Oriented
Concept Tested: Mixed Advanced Problems
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
CBSE Numerical Question 40For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Force on Moving Charge
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Force on Moving Charge
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
CBSE Numerical Question 41A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Board-Oriented
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
CBSE Numerical Question 42A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Circular Motion and Helical Motion
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Board-Oriented
Concept Tested: Circular Motion and Helical Motion
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
CBSE Numerical Question 43Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Board-Oriented
Concept Tested: Biot-Savart Law
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Board-Oriented
Concept Tested: Biot-Savart Law
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
CBSE Numerical Question 44For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
CBSE Numerical Question 45In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
CBSE Numerical Question 46A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Board-Oriented
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
CBSE Numerical Question 47The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Ampere Circuital Law
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Board-Oriented
Concept Tested: Ampere Circuital Law
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
CBSE Numerical Question 48For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Solenoid and Toroid
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Board-Oriented
Concept Tested: Solenoid and Toroid
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
CBSE Numerical Question 49A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Board-Oriented
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
CBSE Numerical Question 50A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Board-Oriented
Concept Tested: Torque on Current Loop
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Board-Oriented
Concept Tested: Torque on Current Loop
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
CBSE Case-Study Questions
Case Study 1Small current element on y-axis
Scenario: A current element dl = dx î, where dx = 1 cm, is placed at the origin and carries current I = 10 A. Find magnetic field at a point on the y-axis at distance 0.5 m.
Data: I = 10 A, dl = 0.01 m, r = 0.5 m, angle = 90°.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Substitute μ₀/4π = 10⁻⁷, I = 10, dl = 10⁻² and r² = 0.25. dB = 10⁻⁷ × 10 × 10⁻² / 0.25 = 4 × 10⁻⁸ T. Direction is obtained by dl × r, along +k̂.
Final: B = 4 × 10⁻⁸ k̂ T.
Data: I = 10 A, dl = 0.01 m, r = 0.5 m, angle = 90°.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Substitute μ₀/4π = 10⁻⁷, I = 10, dl = 10⁻² and r² = 0.25. dB = 10⁻⁷ × 10 × 10⁻² / 0.25 = 4 × 10⁻⁸ T. Direction is obtained by dl × r, along +k̂.
Final: B = 4 × 10⁻⁸ k̂ T.
Case Study 2Two mutually perpendicular long wires
Scenario: Two long insulating wires are mutually perpendicular. Currents 2 A and 1.5 A flow as shown. Point P is 4 cm from the vertical wire and 3 cm from the horizontal wire. Find net magnetic field at P.
Data: I₁ = 2 A, r₁ = 4 cm; I₂ = 1.5 A, r₂ = 3 cm.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: For the vertical wire, B₁ = 2×10⁻⁷ × 2/0.04 = 1×10⁻⁵ T. For the horizontal wire, B₂ = 2×10⁻⁷ × 1.5/0.03 = 1×10⁻⁵ T. The directions are same by right-hand rule, so they add.
Final: B = 2 × 10⁻⁵ T.
Data: I₁ = 2 A, r₁ = 4 cm; I₂ = 1.5 A, r₂ = 3 cm.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: For the vertical wire, B₁ = 2×10⁻⁷ × 2/0.04 = 1×10⁻⁵ T. For the horizontal wire, B₂ = 2×10⁻⁷ × 1.5/0.03 = 1×10⁻⁵ T. The directions are same by right-hand rule, so they add.
Final: B = 2 × 10⁻⁵ T.
Case Study 3Magnetic field at centre of rectangular loop
Scenario: A rectangular loop of sides a and b carries current I. Find magnetic field at its centre O.
Data: Current I, length a, breadth b.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Find contribution of each side using the finite-wire formula. Opposite sides give equal contributions and all directions are same at the centre. Adding four side contributions gives the compact rectangular-loop result.
Final: B = [2μ₀I√(a²+b²)]/(πab), perpendicular to the plane.
Data: Current I, length a, breadth b.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Find contribution of each side using the finite-wire formula. Opposite sides give equal contributions and all directions are same at the centre. Adding four side contributions gives the compact rectangular-loop result.
Final: B = [2μ₀I√(a²+b²)]/(πab), perpendicular to the plane.
Case Study 4Two semi-infinite wires with equal current
Scenario: Two wires CO and OA carry equal currents I and extend to infinity. If ∠AOC = θ, find B at point P on the angle bisector at distance r from O.
Data: Equal current I, angle θ, OP = r on angle bisector.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Use the finite straight conductor expression for both semi-infinite arms. The perpendicular distance from P to either arm is r sin(θ/2). The angular factor gives 1 + cos(θ/2) for each branch. Add both equal contributions.
Final: B = (μ₀/4π) [2I/r] [(1 + cos(θ/2))/sin(θ/2)].
Data: Equal current I, angle θ, OP = r on angle bisector.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Use the finite straight conductor expression for both semi-infinite arms. The perpendicular distance from P to either arm is r sin(θ/2). The angular factor gives 1 + cos(θ/2) for each branch. Add both equal contributions.
Final: B = (μ₀/4π) [2I/r] [(1 + cos(θ/2))/sin(θ/2)].
Case Study 5Three parallel wires at x = 1 m, 2 m and 4 m
Scenario: Equal currents I = 1 A flow through long wires parallel to the y-axis at x = 1 m, 2 m and 4 m. Directions are up, down and up respectively. Find magnetic field at origin.
Data: I = 1 A, distances 1 m, 2 m, 4 m.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: At O, add signed fields due to three wires. The wire at x = 1 m contributes one way, x = 2 m contributes the same way because current is reversed, and x = 4 m contributes opposite. Net coefficient is 1 + 1/2 - 1/4 = 5/4 times 2×10⁻⁷.
Final: B = 2.5 × 10⁻⁷ T with direction fixed by right-hand rule.
Data: I = 1 A, distances 1 m, 2 m, 4 m.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: At O, add signed fields due to three wires. The wire at x = 1 m contributes one way, x = 2 m contributes the same way because current is reversed, and x = 4 m contributes opposite. Net coefficient is 1 + 1/2 - 1/4 = 5/4 times 2×10⁻⁷.
Final: B = 2.5 × 10⁻⁷ T with direction fixed by right-hand rule.
Case Study 6Circular coil with N turns
Scenario: A circular coil of N turns, radius R, carries current I. Find B at centre and at axial distance x.
Data: N, I, R and x.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Use Biot-Savart law. At the centre, all elements contribute same direction. At axial point, transverse components cancel and axial components add.
Final: Bcentre = μ₀NI/2R; Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²].
Data: N, I, R and x.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Use Biot-Savart law. At the centre, all elements contribute same direction. At axial point, transverse components cancel and axial components add.
Final: Bcentre = μ₀NI/2R; Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²].
Case Study 7Field at centre of semicircular arc
Scenario: A current carrying wire is bent into a semicircular arc of radius R. Find magnetic field at the centre.
Data: Current I, radius R, angle π rad.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Straight radial joining parts give zero at the centre if the point lies along their extension. For a semicircle θ = π, so B = μ₀Iπ/4πR.
Final: B = μ₀I/4R, direction by right-hand rule.
Data: Current I, radius R, angle π rad.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Straight radial joining parts give zero at the centre if the point lies along their extension. For a semicircle θ = π, so B = μ₀Iπ/4πR.
Final: B = μ₀I/4R, direction by right-hand rule.
Case Study 8Current density varying as J = kr²
Scenario: In a cylindrical conductor of radius a, current density varies as J = kr². Find magnetic field at distance r from the axis for r < a and r > a.
Data: J = kr², conductor radius a.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: For r < a, I_enclosed = ∫₀ʳ kρ²(2πρ dρ) = πkr⁴/2. Therefore B(2πr)=μ₀πkr⁴/2. For outside, use total current at r=a.
Final: Inside: B = μ₀kr³/4. Outside: B = μ₀ka⁴/(4r).
Data: J = kr², conductor radius a.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: For r < a, I_enclosed = ∫₀ʳ kρ²(2πρ dρ) = πkr⁴/2. Therefore B(2πr)=μ₀πkr⁴/2. For outside, use total current at r=a.
Final: Inside: B = μ₀kr³/4. Outside: B = μ₀ka⁴/(4r).
Case Study 9Field of a long solenoid
Scenario: A long solenoid has length l, total turns N and current I. Find magnetic field inside and near one end.
Data: N turns, length l, current I.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Apply Ampere law to a rectangular loop partly inside and partly outside. Outside field is negligible for a long solenoid. At one end, field is approximately half of central value.
Final: Bcentre = μ₀(N/l)I; Bend ≈ μ₀(N/l)I/2.
Data: N turns, length l, current I.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Apply Ampere law to a rectangular loop partly inside and partly outside. Outside field is negligible for a long solenoid. At one end, field is approximately half of central value.
Final: Bcentre = μ₀(N/l)I; Bend ≈ μ₀(N/l)I/2.
Case Study 10Force between same-direction currents
Scenario: Two long parallel wires separated by distance d carry currents I₁ and I₂ in the same direction. Find force per unit length and state nature.
Data: I₁, I₂, separation d.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Field produced by wire 1 at wire 2 acts perpendicular to current in wire 2. Applying Fleming left hand rule or vector product gives attraction for same directions.
Final: F/L = μ₀I₁I₂/(2πd), attractive.
Data: I₁, I₂, separation d.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Field produced by wire 1 at wire 2 acts perpendicular to current in wire 2. Applying Fleming left hand rule or vector product gives attraction for same directions.
Final: F/L = μ₀I₁I₂/(2πd), attractive.
Case Study 11Current loop in uniform magnetic field
Scenario: A rectangular coil of N turns and area A carries current I in magnetic field B. Find torque.
Data: N, I, A, B, angle θ between magnetic moment and B.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Forces on opposite sides form a couple. Net force is zero but torque is not zero when the magnetic moment is not parallel to B.
Final: τ = NIAB sinθ.
Data: N, I, A, B, angle θ between magnetic moment and B.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Forces on opposite sides form a couple. Net force is zero but torque is not zero when the magnetic moment is not parallel to B.
Final: τ = NIAB sinθ.
Case Study 12Torque balance in MCG
Scenario: A moving coil galvanometer has N turns, area A, field B and torsional constant k. Derive current-deflection relation.
Data: N, A, B, k and deflection θ.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: In radial field, magnetic torque is NBIA independent of angle. At equilibrium NBIA = kθ.
Final: I = kθ/NBA; current sensitivity = NBA/k.
Data: N, A, B, k and deflection θ.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: In radial field, magnetic torque is NBIA independent of angle. At equilibrium NBIA = kθ.
Final: I = kθ/NBA; current sensitivity = NBA/k.
Case Study 13Small current element on y-axis
Scenario: A current element dl = dx î, where dx = 1 cm, is placed at the origin and carries current I = 10 A. Find magnetic field at a point on the y-axis at distance 0.5 m.
Data: I = 10 A, dl = 0.01 m, r = 0.5 m, angle = 90°.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Substitute μ₀/4π = 10⁻⁷, I = 10, dl = 10⁻² and r² = 0.25. dB = 10⁻⁷ × 10 × 10⁻² / 0.25 = 4 × 10⁻⁸ T. Direction is obtained by dl × r, along +k̂.
Final: B = 4 × 10⁻⁸ k̂ T.
Data: I = 10 A, dl = 0.01 m, r = 0.5 m, angle = 90°.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Substitute μ₀/4π = 10⁻⁷, I = 10, dl = 10⁻² and r² = 0.25. dB = 10⁻⁷ × 10 × 10⁻² / 0.25 = 4 × 10⁻⁸ T. Direction is obtained by dl × r, along +k̂.
Final: B = 4 × 10⁻⁸ k̂ T.
Case Study 14Two mutually perpendicular long wires
Scenario: Two long insulating wires are mutually perpendicular. Currents 2 A and 1.5 A flow as shown. Point P is 4 cm from the vertical wire and 3 cm from the horizontal wire. Find net magnetic field at P.
Data: I₁ = 2 A, r₁ = 4 cm; I₂ = 1.5 A, r₂ = 3 cm.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: For the vertical wire, B₁ = 2×10⁻⁷ × 2/0.04 = 1×10⁻⁵ T. For the horizontal wire, B₂ = 2×10⁻⁷ × 1.5/0.03 = 1×10⁻⁵ T. The directions are same by right-hand rule, so they add.
Final: B = 2 × 10⁻⁵ T.
Data: I₁ = 2 A, r₁ = 4 cm; I₂ = 1.5 A, r₂ = 3 cm.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: For the vertical wire, B₁ = 2×10⁻⁷ × 2/0.04 = 1×10⁻⁵ T. For the horizontal wire, B₂ = 2×10⁻⁷ × 1.5/0.03 = 1×10⁻⁵ T. The directions are same by right-hand rule, so they add.
Final: B = 2 × 10⁻⁵ T.
Case Study 15Magnetic field at centre of rectangular loop
Scenario: A rectangular loop of sides a and b carries current I. Find magnetic field at its centre O.
Data: Current I, length a, breadth b.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Find contribution of each side using the finite-wire formula. Opposite sides give equal contributions and all directions are same at the centre. Adding four side contributions gives the compact rectangular-loop result.
Final: B = [2μ₀I√(a²+b²)]/(πab), perpendicular to the plane.
Data: Current I, length a, breadth b.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Find contribution of each side using the finite-wire formula. Opposite sides give equal contributions and all directions are same at the centre. Adding four side contributions gives the compact rectangular-loop result.
Final: B = [2μ₀I√(a²+b²)]/(πab), perpendicular to the plane.
Case Study 16Two semi-infinite wires with equal current
Scenario: Two wires CO and OA carry equal currents I and extend to infinity. If ∠AOC = θ, find B at point P on the angle bisector at distance r from O.
Data: Equal current I, angle θ, OP = r on angle bisector.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Use the finite straight conductor expression for both semi-infinite arms. The perpendicular distance from P to either arm is r sin(θ/2). The angular factor gives 1 + cos(θ/2) for each branch. Add both equal contributions.
Final: B = (μ₀/4π) [2I/r] [(1 + cos(θ/2))/sin(θ/2)].
Data: Equal current I, angle θ, OP = r on angle bisector.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Use the finite straight conductor expression for both semi-infinite arms. The perpendicular distance from P to either arm is r sin(θ/2). The angular factor gives 1 + cos(θ/2) for each branch. Add both equal contributions.
Final: B = (μ₀/4π) [2I/r] [(1 + cos(θ/2))/sin(θ/2)].
Case Study 17Three parallel wires at x = 1 m, 2 m and 4 m
Scenario: Equal currents I = 1 A flow through long wires parallel to the y-axis at x = 1 m, 2 m and 4 m. Directions are up, down and up respectively. Find magnetic field at origin.
Data: I = 1 A, distances 1 m, 2 m, 4 m.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: At O, add signed fields due to three wires. The wire at x = 1 m contributes one way, x = 2 m contributes the same way because current is reversed, and x = 4 m contributes opposite. Net coefficient is 1 + 1/2 - 1/4 = 5/4 times 2×10⁻⁷.
Final: B = 2.5 × 10⁻⁷ T with direction fixed by right-hand rule.
Data: I = 1 A, distances 1 m, 2 m, 4 m.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: At O, add signed fields due to three wires. The wire at x = 1 m contributes one way, x = 2 m contributes the same way because current is reversed, and x = 4 m contributes opposite. Net coefficient is 1 + 1/2 - 1/4 = 5/4 times 2×10⁻⁷.
Final: B = 2.5 × 10⁻⁷ T with direction fixed by right-hand rule.
Case Study 18Circular coil with N turns
Scenario: A circular coil of N turns, radius R, carries current I. Find B at centre and at axial distance x.
Data: N, I, R and x.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Use Biot-Savart law. At the centre, all elements contribute same direction. At axial point, transverse components cancel and axial components add.
Final: Bcentre = μ₀NI/2R; Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²].
Data: N, I, R and x.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Use Biot-Savart law. At the centre, all elements contribute same direction. At axial point, transverse components cancel and axial components add.
Final: Bcentre = μ₀NI/2R; Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²].
Case Study 19Field at centre of semicircular arc
Scenario: A current carrying wire is bent into a semicircular arc of radius R. Find magnetic field at the centre.
Data: Current I, radius R, angle π rad.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Straight radial joining parts give zero at the centre if the point lies along their extension. For a semicircle θ = π, so B = μ₀Iπ/4πR.
Final: B = μ₀I/4R, direction by right-hand rule.
Data: Current I, radius R, angle π rad.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: Straight radial joining parts give zero at the centre if the point lies along their extension. For a semicircle θ = π, so B = μ₀Iπ/4πR.
Final: B = μ₀I/4R, direction by right-hand rule.
Case Study 20Current density varying as J = kr²
Scenario: In a cylindrical conductor of radius a, current density varies as J = kr². Find magnetic field at distance r from the axis for r < a and r > a.
Data: J = kr², conductor radius a.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: For r < a, I_enclosed = ∫₀ʳ kρ²(2πρ dρ) = πkr⁴/2. Therefore B(2πr)=μ₀πkr⁴/2. For outside, use total current at r=a.
Final: Inside: B = μ₀kr³/4. Outside: B = μ₀ka⁴/(4r).
Data: J = kr², conductor radius a.
Questions: identify direction of B, choose correct formula, calculate magnitude and explain one common error.
Complete Solution: For r < a, I_enclosed = ∫₀ʳ kρ²(2πρ dρ) = πkr⁴/2. Therefore B(2πr)=μ₀πkr⁴/2. For outside, use total current at r=a.
Final: Inside: B = μ₀kr³/4. Outside: B = μ₀ka⁴/(4r).
NEET Tough MCQs
NEET Question 1A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
NEET Question 2A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
NEET Question 3Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
NEET Question 4For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
NEET Question 5In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
NEET Question 6A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
NEET Question 7The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
NEET Question 8For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
NEET Question 9A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
NEET Question 10A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
NEET Question 11Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
NEET Question 12For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
NEET Question 13In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
NEET Question 14A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
NEET Question 15The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
NEET Question 16For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
NEET Question 17A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
NEET Question 18A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
NEET Question 19Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
NEET Question 20For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
NEET Question 21In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
NEET Question 22A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
NEET Question 23The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
NEET Question 24For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Torque on Current Loop
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium
Concept Tested: Torque on Current Loop
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
NEET Question 25A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Moving Coil Galvanometer
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium
Concept Tested: Moving Coil Galvanometer
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
NEET Question 26A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Mixed Advanced Problems
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium
Concept Tested: Mixed Advanced Problems
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
NEET Question 27Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
NEET Question 28For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
NEET Question 29In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
NEET Question 30A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
NEET Question 31The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
NEET Question 32For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
NEET Question 33A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
NEET Question 34A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
NEET Question 35Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
NEET Question 36For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
NEET Question 37In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Torque on Current Loop
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium
Concept Tested: Torque on Current Loop
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
NEET Question 38A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Moving Coil Galvanometer
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium
Concept Tested: Moving Coil Galvanometer
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
NEET Question 39The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Mixed Advanced Problems
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium
Concept Tested: Mixed Advanced Problems
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
NEET Question 40For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
NEET Question 41A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
NEET Question 42A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
NEET Question 43Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
NEET Question 44For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
NEET Question 45In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
NEET Question 46A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
NEET Question 47The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
NEET Question 48For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
NEET Question 49A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
NEET Question 50A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Torque on Current Loop
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium
Concept Tested: Torque on Current Loop
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
NEET Question 51Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium
Concept Tested: Moving Coil Galvanometer
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium
Concept Tested: Moving Coil Galvanometer
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
NEET Question 52For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Mixed Advanced Problems
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium
Concept Tested: Mixed Advanced Problems
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
NEET Question 53In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
NEET Question 54A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
NEET Question 55The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
NEET Question 56For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
NEET Question 57A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
NEET Question 58A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
NEET Question 59Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
NEET Question 60For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
NEET Question 61In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
NEET Question 62A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
NEET Question 63The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Torque on Current Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium
Concept Tested: Torque on Current Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
NEET Question 64For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Moving Coil Galvanometer
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium
Concept Tested: Moving Coil Galvanometer
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
NEET Question 65A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Mixed Advanced Problems
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium
Concept Tested: Mixed Advanced Problems
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
NEET Question 66A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
NEET Question 67Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
NEET Question 68For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
NEET Question 69In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
NEET Question 70A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
NEET Question 71The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
NEET Question 72For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
NEET Question 73A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
NEET Question 74A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
NEET Question 75Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
NEET Question 76For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Torque on Current Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium
Concept Tested: Torque on Current Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
NEET Question 77In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Moving Coil Galvanometer
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium
Concept Tested: Moving Coil Galvanometer
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
NEET Question 78A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Mixed Advanced Problems
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium
Concept Tested: Mixed Advanced Problems
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
NEET Question 79The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
NEET Question 80For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
NEET Question 81A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
NEET Question 82A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
NEET Question 83Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
NEET Question 84For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
NEET Question 85In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
NEET Question 86A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
NEET Question 87The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
NEET Question 88For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
NEET Question 89A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Torque on Current Loop
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium
Concept Tested: Torque on Current Loop
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
NEET Question 90A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Moving Coil Galvanometer
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium
Concept Tested: Moving Coil Galvanometer
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
NEET Question 91Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium
Concept Tested: Mixed Advanced Problems
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium
Concept Tested: Mixed Advanced Problems
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
NEET Question 92For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium
Concept Tested: Magnetic Force on Moving Charge
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
NEET Question 93In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
NEET Question 94A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium
Concept Tested: Circular Motion and Helical Motion
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
NEET Question 95The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium
Concept Tested: Biot-Savart Law
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
NEET Question 96For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
NEET Question 97A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
NEET Question 98A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
NEET Question 99Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium
Concept Tested: Ampere Circuital Law
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
NEET Question 100For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium
Concept Tested: Solenoid and Toroid
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Main MCQs
JEE Main Question 1A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Main Question 2A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Main Question 3Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Main Question 4For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Main Question 5In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Main Question 6A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Main Question 7The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Main Question 8For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Main Question 9A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Main Question 10A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium-Difficult
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Main Question 11Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium-Difficult
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium-Difficult
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Main Question 12For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium-Difficult
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Main Question 13In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium-Difficult
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Main Question 14A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Main Question 15The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Main Question 16For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Main Question 17A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Main Question 18A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Main Question 19Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Main Question 20For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Main Question 21In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Main Question 22A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Main Question 23The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium-Difficult
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Main Question 24For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Torque on Current Loop
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium-Difficult
Concept Tested: Torque on Current Loop
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Main Question 25A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Moving Coil Galvanometer
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium-Difficult
Concept Tested: Moving Coil Galvanometer
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Main Question 26A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Mixed Advanced Problems
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium-Difficult
Concept Tested: Mixed Advanced Problems
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Main Question 27Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Main Question 28For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Main Question 29In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Main Question 30A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Main Question 31The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Main Question 32For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Main Question 33A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Main Question 34A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Main Question 35Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Main Question 36For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium-Difficult
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Main Question 37In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Torque on Current Loop
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium-Difficult
Concept Tested: Torque on Current Loop
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Main Question 38A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Moving Coil Galvanometer
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium-Difficult
Concept Tested: Moving Coil Galvanometer
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Main Question 39The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Mixed Advanced Problems
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium-Difficult
Concept Tested: Mixed Advanced Problems
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Main Question 40For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Main Question 41A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Main Question 42A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Main Question 43Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Main Question 44For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Main Question 45In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Main Question 46A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Main Question 47The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Main Question 48For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Main Question 49A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium-Difficult
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Main Question 50A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Torque on Current Loop
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium-Difficult
Concept Tested: Torque on Current Loop
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Main Question 51Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium-Difficult
Concept Tested: Moving Coil Galvanometer
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium-Difficult
Concept Tested: Moving Coil Galvanometer
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Main Question 52For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Mixed Advanced Problems
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium-Difficult
Concept Tested: Mixed Advanced Problems
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Main Question 53In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Main Question 54A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Main Question 55The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Main Question 56For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Main Question 57A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Main Question 58A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Main Question 59Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Main Question 60For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Main Question 61In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Main Question 62A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium-Difficult
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Main Question 63The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Torque on Current Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium-Difficult
Concept Tested: Torque on Current Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Main Question 64For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Moving Coil Galvanometer
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium-Difficult
Concept Tested: Moving Coil Galvanometer
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Main Question 65A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Mixed Advanced Problems
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium-Difficult
Concept Tested: Mixed Advanced Problems
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Main Question 66A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Main Question 67Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Main Question 68For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Main Question 69In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Main Question 70A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Main Question 71The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Main Question 72For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Main Question 73A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Main Question 74A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Main Question 75Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium-Difficult
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium-Difficult
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Main Question 76For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Torque on Current Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium-Difficult
Concept Tested: Torque on Current Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Main Question 77In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Moving Coil Galvanometer
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium-Difficult
Concept Tested: Moving Coil Galvanometer
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Main Question 78A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Mixed Advanced Problems
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium-Difficult
Concept Tested: Mixed Advanced Problems
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Main Question 79The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Main Question 80For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Main Question 81A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Main Question 82A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Main Question 83Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Main Question 84For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Main Question 85In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Main Question 86A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Main Question 87The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Main Question 88For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium-Difficult
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Main Question 89A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Torque on Current Loop
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium-Difficult
Concept Tested: Torque on Current Loop
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Main Question 90A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Moving Coil Galvanometer
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium-Difficult
Concept Tested: Moving Coil Galvanometer
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Main Question 91Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium-Difficult
Concept Tested: Mixed Advanced Problems
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium-Difficult
Concept Tested: Mixed Advanced Problems
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Main Question 92For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Force on Moving Charge
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Main Question 93In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Medium-Difficult
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Main Question 94A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Medium-Difficult
Concept Tested: Circular Motion and Helical Motion
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Main Question 95The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Medium-Difficult
Concept Tested: Biot-Savart Law
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Main Question 96For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Main Question 97A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Main Question 98A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Medium-Difficult
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Main Question 99Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Medium-Difficult
Concept Tested: Ampere Circuital Law
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Main Question 100For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Medium-Difficult
Concept Tested: Solenoid and Toroid
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Single Correct Questions
JEE Advanced Single Correct Question 1A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Single Correct Question 2A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Single Correct Question 3Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Single Correct Question 4For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Single Correct Question 5In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Single Correct Question 6A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Single Correct Question 7The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Advanced Single Correct Question 8For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Advanced Single Correct Question 9A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Single Correct Question 10A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Single Correct Question 11Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Single Correct Question 12For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Single Correct Question 13In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Single Correct Question 14A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Single Correct Question 15The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Advanced Single Correct Question 16For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Advanced Single Correct Question 17A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Single Correct Question 18A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Single Correct Question 19Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Single Correct Question 20For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Single Correct Question 21In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Single Correct Question 22A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Single Correct Question 23The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Advanced Single Correct Question 24For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Advanced Single Correct Question 25A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Single Correct Question 26A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Single Correct Question 27Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Single Correct Question 28For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Single Correct Question 29In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Single Correct Question 30A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Single Correct Question 31The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Advanced Single Correct Question 32For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Advanced Single Correct Question 33A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Single Correct Question 34A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Single Correct Question 35Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Single Correct Question 36For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Single Correct Question 37In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Single Correct Question 38A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Single Correct Question 39The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Advanced Single Correct Question 40For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Advanced Multiple Correct Questions
JEE Advanced Multiple Correct Question 1A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Multiple Correct Question 2A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Multiple Correct Question 3Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Multiple Correct Question 4For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Multiple Correct Question 5In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Multiple Correct Question 6A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Multiple Correct Question 7The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Advanced Multiple Correct Question 8For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Advanced Multiple Correct Question 9A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Multiple Correct Question 10A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Multiple Correct Question 11Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Multiple Correct Question 12For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Multiple Correct Question 13In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Multiple Correct Question 14A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Multiple Correct Question 15The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Advanced Multiple Correct Question 16For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Advanced Multiple Correct Question 17A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Multiple Correct Question 18A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Multiple Correct Question 19Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Multiple Correct Question 20For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Multiple Correct Question 21In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Multiple Correct Question 22A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Multiple Correct Question 23The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Advanced Multiple Correct Question 24For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Advanced Multiple Correct Question 25A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Multiple Correct Question 26A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Multiple Correct Question 27Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Multiple Correct Question 28For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Multiple Correct Question 29In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Multiple Correct Question 30A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Integer-Type Questions
JEE Advanced Integer Question 1A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Integer Question 2A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Integer Question 3Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Integer Question 4For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Integer Question 5In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Integer Question 6A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Integer Question 7The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Advanced Integer Question 8For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Advanced Integer Question 9A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Integer Question 10A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Integer Question 11Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Integer Question 12For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Integer Question 13In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Integer Question 14A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Integer Question 15The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Advanced Integer Question 16For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Advanced Integer Question 17A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Integer Question 18A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Integer Question 19Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Integer Question 20For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Matrix-Match Questions
JEE Advanced Matrix Match Question 1A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Matrix Match Question 2A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Matrix Match Question 3Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Matrix Match Question 4For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Matrix Match Question 5In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Matrix Match Question 6A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Matrix Match Question 7The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Advanced Matrix Match Question 8For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Advanced Matrix Match Question 9A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Matrix Match Question 10A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Matrix Match Question 11Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Matrix Match Question 12For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Matrix Match Question 13In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Matrix Match Question 14A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Matrix Match Question 15The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Advanced Paragraph-Type Questions
JEE Advanced Paragraph Question 1A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Paragraph Question 2A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Paragraph Question 3Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Circular Motion and Helical Motion
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Paragraph Question 4For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Biot-Savart Law
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Paragraph Question 5In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Straight Wire
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Paragraph Question 6A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field due to Circular Coil
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Paragraph Question 7The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Field on Axis of Circular Loop
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
JEE Advanced Paragraph Question 8For a current density J = kr² in a cylindrical conductor, magnetic field inside varies as
A) r³
B) r
C) 1/r
D) constant
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Ampere Circuital Law
Formula Used: ∮B·dl = μ₀I_enclosed
Detailed Explanation: I_enclosed ∝ ∫r²(2πr dr) ∝ r⁴. Ampere law gives B×2πr ∝ r⁴, hence B ∝ r³.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Uniform current density gives B ∝ r; this problem is not uniform.
JEE Advanced Paragraph Question 9A charged particle enters a uniform magnetic field with velocity making angle θ with B. Which quantity remains unchanged during motion?
A) Speed
B) Velocity vector
C) Linear momentum vector
D) Kinetic energy only at θ = 90°
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Solenoid and Toroid
Formula Used: F = qvB sinθ
Detailed Explanation: Magnetic force is perpendicular to velocity, so it does no work. Speed and kinetic energy remain constant, while direction of velocity may change.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Students often say velocity remains constant; only speed remains constant.
JEE Advanced Paragraph Question 10A long straight wire carries current I. If distance from the wire is doubled and current is tripled, magnetic field becomes
A) 3B/2
B) 2B/3
C) 6B
D) B/6
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Force Between Parallel Current Carrying Conductors
Formula Used: B = μ₀I/2πr
Detailed Explanation: B ∝ I/r. New B = (3I)/(2r) compared to I/r = 3B/2.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not use inverse-square law for a long straight wire.
JEE Advanced Paragraph Question 11Two long parallel wires carry currents in opposite directions. The force between them is
A) Attractive
B) Repulsive
C) Zero
D) Depends only on length
Correct Answer: B
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Torque on Current Loop
Formula Used: F/L = μ₀I₁I₂/2πd
Detailed Explanation: Same direction currents attract; opposite direction currents repel.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Confusing magnetic field direction with force direction.
JEE Advanced Paragraph Question 12For a circular coil, field on its axis at distance x is proportional to
A) R²/(R²+x²)³ᐟ²
B) R/(R²+x²)
C) 1/x² always
D) R³/(R²+x²)
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Moving Coil Galvanometer
Formula Used: Baxis = μ₀NIR²/[2(R²+x²)³ᐟ²]
Detailed Explanation: Biot-Savart law gives axial field B = μ₀NIR²/[2(R²+x²)³ᐟ²].
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: At x = 0, use centre formula; far away, dipole-like decrease appears.
JEE Advanced Paragraph Question 13In a moving coil galvanometer, radial magnetic field is used so that
A) Torque is proportional to current
B) Current becomes zero
C) Magnetic field becomes zero
D) Coil area changes
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Mixed Advanced Problems
Formula Used: NBIA = kθ
Detailed Explanation: Radial field keeps plane of coil parallel to B, so sinα = 1 and τ = NBIA.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Do not write τ = NBIA sinθ in radial field derivation.
JEE Advanced Paragraph Question 14A solenoid has 5 layers of turns. If total turns per unit length become five times, central field becomes
A) 5 times
B) 25 times
C) 1/5 times
D) unchanged
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Magnetic Force on Moving Charge
Formula Used: B = μ₀nI
Detailed Explanation: For a long solenoid B = μ₀nI; field is directly proportional to turns per unit length.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Area of solenoid does not enter ideal long solenoid formula.
JEE Advanced Paragraph Question 15The pitch of a charged particle executing helical motion in magnetic field is
A) v_parallel T
B) v_perpendicular T
C) qB/2πm
D) mv/qB
Correct Answer: A
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
Difficulty Level: Difficult / JEE Advanced
Concept Tested: Motion of Charged Particle in Magnetic Field
Formula Used: p = v cosθ × 2πm/qB
Detailed Explanation: Parallel velocity is unaffected by magnetic force; distance advanced in one period is pitch = v_parallel T.
Shortcut Method: Identify proportionality first, then substitute ratios before doing long calculation.
Why other options are wrong: The remaining options ignore direction, proportionality or the correct limiting formula.
Common Student Mistake: Radius uses perpendicular velocity; pitch uses parallel velocity.
IB Physics Structured Questions
IB Physics Subjective 1Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 2Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 3Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 4Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 5Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 6Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 7Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 8Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 9Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 10Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 11Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 12Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 13Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 14Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 15Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 16Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 17Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 18Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 19Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 20Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 21Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 22Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 23Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 24Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 25Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 26Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 27Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 28Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 29Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
IB Physics Subjective 30Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for IB Physics.
ICSE / IGCSE Diagram-Based Questions
ICSE / IGCSE Subjective 1Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 2Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 3Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 4Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 5Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 6Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 7Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 8Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 9Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 10Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 11Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 12Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 13Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 14Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 15Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 16Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 17Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 18Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 19Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 20Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 21Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 22Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 23Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 24Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 25Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 26Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 27Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 28Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 29Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
ICSE / IGCSE Subjective 30Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for ICSE / IGCSE.
British Curriculum / A-Level Questions
A-Level Physics Subjective 1Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 2Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 3Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 4Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 5Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 6Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 7Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 8Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 9Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 10Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 11Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 12Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 13Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 14Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 15Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 16Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 17Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 18Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 19Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 20Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 21Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 22Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 23Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 24Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 25Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 26Write a structured answer to derive magnetic field due to a long straight conductor using Ampere law.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 27Write a structured answer to derive force per unit length between two parallel current carrying conductors.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 28Write a structured answer to explain radial magnetic field in a moving coil galvanometer.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 29Write a structured answer to derive magnetic field on the axis of a circular current loop.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
A-Level Physics Subjective 30Write a structured answer to compare circular motion and helical motion of a charged particle.
Answer: Start with a neat labeled diagram. State the law used, define all symbols, write vector direction by right-hand rule, complete the mathematical derivation and box the final result. Add one line of physical meaning and one common mistake. This is the expected board-style answer pattern for A-Level Physics.
Final Revision Section
NEET Traps
Do not ignore direction. Use dot/cross convention and proportionality shortcuts.
JEE Traps
Finite wire, arcs, mixed straight-curved conductors and non-uniform current density need integration or Ampere law carefully.
CBSE Derivations
Lorentz force, circular motion, Biot-Savart, Ampere law, force between wires, torque on loop and MCG are high-value.
Diagram Revision
Always show current direction, B direction, force direction, labels and distances clearly.
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