Ampere's Circuital Law and Solenoid - Complete Physics Guide

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Ampere’s Circuital Law and Solenoid

A complete premium Physics guide by Kumar Sir covering Ampere’s Law, straight wire derivation, solid cylindrical conductor, long solenoid, solenoid end field, solenoid as magnetic dipole, toroid, formulas, graphs and exam-level ampere circuital law and solenoid questions.

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1. Ampere’s Circuital Law

The line integral of magnetic field around any closed path is equal to μ₀ times the net current enclosed by that path.

Magnetic field form∮ B · dℓ = μ₀ I_enclosed
Magnetic intensity form∮ H · dℓ = I_enclosed

The closed path is called an Amperian path. dℓ is a small directed length element along the chosen path. The direction is chosen by the right-hand thumb rule: curl fingers along the path and thumb gives positive current direction.

Ampere's Circuital Law: closed Amperian path enclosing current
I_enclosed dℓ B circulation ∮ B · dℓ = μ₀ I_enclosed
DerivationCBSE • NEET • JEE

2. Derivation Using a Long Straight Current-Carrying Conductor

Long straight wire and circular Amperian loop
current I r B = μ₀I/2πr and ∮dℓ = 2πr
Given / Symbols:
Long straight wire carrying current I, circular Amperian path of radius r.
1Magnetic field at distance r from long straight wire is B = μ₀I/2πr.
2Choose a circular Amperian path centred on the wire.
3By symmetry B is constant on the circle and parallel to dℓ.
4Therefore ∮B·dℓ = B∮dℓ.
5The circumference is ∮dℓ = 2πr.
6So ∮B·dℓ = μ₀I/2πr × 2πr.
7Thus ∮B·dℓ = μ₀I.
Final Result:∮ B · dℓ = μ₀I
Common mistake:
Do not use this simple step for low-symmetry finite wires.

3. Validity and Conditions of Ampere’s Law

Most useful for high symmetry.
Works directly for infinite straight conductor, long solenoid, toroid, infinite current sheet and cylindrical conductor.
B should be constant or easily expressible along the chosen path.
Not convenient for arbitrary finite wires.
For time-varying electric fields, Maxwell's correction is required.
At school level it is used for steady currents in magnetostatics.
DerivationCBSE • NEET • JEE

4. Application: Solid Cylindrical Conductor

Solid cylindrical conductor: inside, surface and outside Amperian loops
I uniform r<R r>R radius R RrB B rises linearly inside, maximum at R, then falls as 1/r
Given / Symbols:
Cylinder radius R carries uniformly distributed current I. Amperian loop radius is r.
1Current density J = I/πR².
2For r
3Ampere's Law gives B(2πr)=μ₀Ir²/R².
4Therefore inside: B = μ₀Ir/2πR².
5At r=R: B = μ₀I/2πR.
6For r>R, I_enclosed=I.
7Therefore outside: B = μ₀I/2πr.
Final Result:Inside: B = μ₀Ir/2πR²; Surface: B = μ₀I/2πR; Outside: B = μ₀I/2πr
Common mistake:
Inside the cylinder never use total current I unless r=R.
DerivationCBSE • NEET • JEE

5. Application: Long Solenoid

Long solenoid with rectangular Amperian loop
uniform B inside Amperian rectangle length l, turns enclosed = nl B l = μ₀(nl)I ⇒ B = μ₀nI
Given / Symbols:
Long solenoid, current I, turns per unit length n, rectangular Amperian loop length l.
1A long solenoid has many closely spaced turns.
2Choose a rectangular Amperian loop with one long side inside the solenoid.
3Outside field is nearly zero for an ideal long solenoid.
4Inside field is uniform and parallel to dℓ.
5Line integral becomes ∮B·dℓ = Bl.
6Number of turns enclosed = nl.
7Current enclosed = nlI.
8Ampere's Law gives Bl = μ₀nlI.
9Therefore B = μ₀nI.
Final Result:B = μ₀nI
Common mistake:
Do not write μ₀NI unless N is turns per unit length times length has been handled.

6. Magnetic Field at the End of Solenoid

Magnetic field at centre and end of a long solenoid
centre: B = μ₀nI end: B = μ₀nI/2 centre end At the end, only one side contributes symmetrically, so field is half
Centre of long solenoidB_center = μ₀nI
End of long solenoidB_end = μ₀nI / 2

At the end, field becomes half of central field because only one side of the long solenoid contributes symmetrically.

7. Solenoid as a Magnetic Dipole

Solenoid behaves like a magnetic dipole
SN m = NIA Field lines emerge from North outside and enter South outside

A current-carrying solenoid behaves like a bar magnet. One end acts like North pole and the other like South pole. Magnetic field lines are nearly uniform inside and return outside.

Magnetic dipole momentm = NIA
Meaning

N = total turns, I = current, A = cross-sectional area.

DerivationCBSE • NEET • JEE

8. Application: Toroid

Toroid and circular Amperian path
r B(2πr) = μ₀NI Inside core: B = μ₀NI/2πr; central and outside regions ≈ 0
Given / Symbols:
Toroid has N turns and current I. Choose circular Amperian path of radius r in the core.
1A toroid is a solenoid bent into a circular ring.
2Choose a circular Amperian loop inside the core.
3By symmetry B is tangential and nearly constant on this path.
4Line integral is ∮B·dℓ = B(2πr).
5Current enclosed = NI.
6Ampere's Law gives B(2πr)=μ₀NI.
7Therefore B = μ₀NI/2πr.
8Since n=N/2πr, B=μ₀nI.
9Outside the toroid and in the empty central region, field is nearly zero for an ideal toroid.
Final Result:B = μ₀NI/2πr = μ₀nI
Common mistake:
Do not use solenoid length formula blindly; for toroid the path length is 2πr.

9. Comparison Table

ApplicationFormulaValid RegionImportant Point
Long straight wireB = μ₀I/2πroutside wirecircular symmetry
Cylinder insideB = μ₀Ir/2πR²r < RI_enclosed = Ir²/R²
Cylinder surfaceB = μ₀I/2πRr = Rmaximum value
Cylinder outsideB = μ₀I/2πrr > Racts like thin wire
Long solenoid centreB = μ₀nIinside centreuniform field
Solenoid endB = μ₀nI/2end of long solenoidhalf of centre
Toroid insideB = μ₀NI/2πrcore regionfield confined
Toroid outsideB ≈ 0outsideideal toroid leakage negligible

10. Common Student Mistakes

Mistake 1Forgetting current enclosed.

Correction: First draw Amperian path, then identify symmetry and enclosed current.

Mistake 2Using total current for inside solid cylinder.

Correction: First draw Amperian path, then identify symmetry and enclosed current.

Mistake 3Confusing r and R.

Correction: First draw Amperian path, then identify symmetry and enclosed current.

Mistake 4Drawing wrong B-r graph.

Correction: First draw Amperian path, then identify symmetry and enclosed current.

Mistake 5Writing solenoid field as μ₀NI instead of μ₀nI.

Correction: First draw Amperian path, then identify symmetry and enclosed current.

Mistake 6Forgetting n=N/L for solenoid.

Correction: First draw Amperian path, then identify symmetry and enclosed current.

Mistake 7Forgetting n=N/2πr for toroid.

Correction: First draw Amperian path, then identify symmetry and enclosed current.

Mistake 8Confusing solenoid and toroid.

Correction: First draw Amperian path, then identify symmetry and enclosed current.

Mistake 9Wrong magnetic field direction.

Correction: First draw Amperian path, then identify symmetry and enclosed current.

Mistake 10Misusing Ampere's Law in low-symmetry situations.

Correction: First draw Amperian path, then identify symmetry and enclosed current.

11. Exam Question Bank With Solutions

A. CBSE Board Questions

CBSE Theory Question 1State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 2Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 3Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 4Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 5Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 6Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 7Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 8Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 9State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 10Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 11Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 12Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 13Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 14Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 15Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 16Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 17State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 18Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 19Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 20Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 21Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 22Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 23Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 24Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Theory Question 25State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 1State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 2Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 3Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 4Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 5Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 6Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 7Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 8Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 9State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 10Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 11Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 12Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 13Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 14Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 15Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 16Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 17State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 18Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 19Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Derivation Derivation 20Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 1State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 2Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 3Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 4Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 5Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 6Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 7Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 8Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 9State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 10Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 11Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 12Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 13Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 14Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 15Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 16Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 17State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 18Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 19Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 20Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 21Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 22Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 23Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 24Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Numerical Numerical 25State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Case Case 1State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Case Case 2Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Case Case 3Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Case Case 4Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Case Case 5Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Case Case 6Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Case Case 7Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Case Case 8Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Case Case 9State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
CBSE Case Case 10Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.

B. NEET Questions

NEET Q1Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q2For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q3Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q4Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q5At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q6For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q7Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q8The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q9For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q10For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q11Variant 2: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q12Variant 2: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q13Variant 2: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q14Variant 2: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q15Variant 2: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q16Variant 2: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q17Variant 2: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q18Variant 2: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q19Variant 2: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q20Variant 2: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q21Variant 3: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q22Variant 3: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q23Variant 3: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q24Variant 3: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q25Variant 3: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q26Variant 3: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q27Variant 3: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q28Variant 3: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q29Variant 3: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q30Variant 3: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q31Variant 4: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q32Variant 4: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q33Variant 4: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q34Variant 4: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q35Variant 4: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q36Variant 4: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q37Variant 4: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q38Variant 4: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q39Variant 4: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q40Variant 4: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q41Variant 5: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q42Variant 5: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q43Variant 5: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q44Variant 5: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q45Variant 5: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q46Variant 5: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q47Variant 5: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q48Variant 5: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q49Variant 5: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q50Variant 5: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q51Variant 6: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q52Variant 6: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q53Variant 6: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q54Variant 6: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q55Variant 6: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q56Variant 6: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q57Variant 6: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q58Variant 6: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q59Variant 6: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q60Variant 6: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q61Variant 7: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q62Variant 7: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q63Variant 7: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q64Variant 7: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q65Variant 7: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q66Variant 7: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q67Variant 7: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q68Variant 7: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q69Variant 7: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q70Variant 7: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q71Variant 8: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q72Variant 8: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q73Variant 8: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q74Variant 8: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
NEET Q75Variant 8: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.

C. JEE Main Questions

JEE Main Q1Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q2For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q3Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q4Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q5At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q6For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q7Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q8The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q9For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q10For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q11Variant 2: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q12Variant 2: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q13Variant 2: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q14Variant 2: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q15Variant 2: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q16Variant 2: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q17Variant 2: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q18Variant 2: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q19Variant 2: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q20Variant 2: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q21Variant 3: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q22Variant 3: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q23Variant 3: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q24Variant 3: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q25Variant 3: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q26Variant 3: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q27Variant 3: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q28Variant 3: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q29Variant 3: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q30Variant 3: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q31Variant 4: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q32Variant 4: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q33Variant 4: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q34Variant 4: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q35Variant 4: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q36Variant 4: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q37Variant 4: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q38Variant 4: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q39Variant 4: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q40Variant 4: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q41Variant 5: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q42Variant 5: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q43Variant 5: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q44Variant 5: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q45Variant 5: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q46Variant 5: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q47Variant 5: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q48Variant 5: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q49Variant 5: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q50Variant 5: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q51Variant 6: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q52Variant 6: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q53Variant 6: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q54Variant 6: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q55Variant 6: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q56Variant 6: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q57Variant 6: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q58Variant 6: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q59Variant 6: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q60Variant 6: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q61Variant 7: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q62Variant 7: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q63Variant 7: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q64Variant 7: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q65Variant 7: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q66Variant 7: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q67Variant 7: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q68Variant 7: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q69Variant 7: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q70Variant 7: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q71Variant 8: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q72Variant 8: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q73Variant 8: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q74Variant 8: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Main Q75Variant 8: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.

D. JEE Advanced Questions

JEE Advanced Single Correct Q1Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q2For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q3Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q4Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q5At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q6For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q7Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q8The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q9For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q10For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q11Variant 2: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q12Variant 2: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q13Variant 2: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q14Variant 2: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q15Variant 2: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q16Variant 2: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q17Variant 2: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q18Variant 2: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q19Variant 2: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q20Variant 2: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q21Variant 3: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q22Variant 3: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q23Variant 3: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q24Variant 3: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q25Variant 3: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q26Variant 3: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q27Variant 3: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q28Variant 3: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q29Variant 3: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Single Correct Q30Variant 3: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q1Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q2For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q3Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q4Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q5At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q6For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q7Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q8The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q9For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q10For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q11Variant 2: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q12Variant 2: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q13Variant 2: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q14Variant 2: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q15Variant 2: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q16Variant 2: For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q17Variant 2: Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q18Variant 2: The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q19Variant 2: For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Multiple Correct Q20Variant 2: For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q1Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q2For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q3Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q4Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q5At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q6For a toroid inside the core, B equals
  1. μ₀NI/2πr
  2. μ₀nI/2
  3. μ₀I/2R
  4. μ₀IR
Correct Answer: A
Detailed Explanation: Use circular Amperian loop: B(2πr)=μ₀NI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q7Ampere's Law is easiest to use when there is
  1. low symmetry
  2. high symmetry
  3. no current
  4. only charge at rest
Correct Answer: B
Detailed Explanation: It is most useful for long straight wire, solenoid, toroid and cylinders.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q8The quantity I_enclosed means
  1. total current anywhere
  2. current linked by chosen Amperian path
  3. current outside path
  4. voltage enclosed
Correct Answer: B
Detailed Explanation: Only current passing through the surface bounded by the path counts.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q9For a solenoid, n is
  1. N/L
  2. NL
  3. N/I
  4. I/N
Correct Answer: A
Detailed Explanation: n is turns per unit length.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q10For a toroid, field outside is approximately
  1. maximum
  2. zero
  3. μ₀NI
  4. infinite
Correct Answer: B
Detailed Explanation: Ideal toroid confines magnetic field mainly inside the core.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q11Variant 2: Ampere's Circuital Law is
  1. ∮B·dℓ = μ₀I_enclosed
  2. B = μ₀I/4πr
  3. F = qvB
  4. E = IR
Correct Answer: A
Detailed Explanation: The law relates circulation of B around a closed path to enclosed current.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q12Variant 2: For a long solenoid, magnetic field inside is
  1. μ₀NI
  2. μ₀nI
  3. μ₀I/2πr
  4. zero
Correct Answer: B
Detailed Explanation: For turns per unit length n, B = μ₀nI.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q13Variant 2: Inside a uniformly current-carrying solid cylinder, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: A
Detailed Explanation: I_enclosed = Ir²/R² and B(2πr)=μ₀I_enclosed, so B∝r.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q14Variant 2: Outside a long solid cylindrical conductor, B varies as
  1. r
  2. 1/r
  3. r²
  4. constant
Correct Answer: B
Detailed Explanation: Outside, all current I is enclosed, giving B=μ₀I/2πr.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Integer Type Q15Variant 2: At the end of a very long solenoid, field is approximately
  1. μ₀nI
  2. μ₀nI/2
  3. 2μ₀nI
  4. zero always
Correct Answer: B
Detailed Explanation: End field is half the central field for an ideal long solenoid.
Common Student Mistake: Check symmetry and enclosed current before choosing formula.
JEE Advanced Matrix Match Matrix 1State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Matrix Match Matrix 2Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Matrix Match Matrix 3Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Matrix Match Matrix 4Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Matrix Match Matrix 5Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Matrix Match Matrix 6Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Matrix Match Matrix 7Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Matrix Match Matrix 8Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Matrix Match Matrix 9State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Matrix Match Matrix 10Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Paragraph Paragraph 1State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Paragraph Paragraph 2Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Paragraph Paragraph 3Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Paragraph Paragraph 4Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Paragraph Paragraph 5Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Paragraph Paragraph 6Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Paragraph Paragraph 7Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Paragraph Paragraph 8Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Paragraph Paragraph 9State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
JEE Advanced Paragraph Paragraph 10Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.

E. IB Physics Questions

IB Structured 1State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 2Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 3Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 4Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 5Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 6Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 7Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 8Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 9State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 10Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 11Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 12Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 13Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 14Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 15Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 16Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 17State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 18Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 19Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 20Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 21Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 22Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 23Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 24Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IB Structured 25State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.

F. ICSE Physics Questions

ICSE Question 1State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 2Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 3Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 4Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 5Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 6Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 7Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 8Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 9State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 10Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 11Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 12Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 13Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 14Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 15Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 16Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 17State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 18Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 19Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 20Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 21Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 22Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 23Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 24Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
ICSE Question 25State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.

G. IGCSE Physics Questions

IGCSE Question 1State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 2Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 3Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 4Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 5Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 6Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 7Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 8Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 9State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 10Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 11Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 12Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 13Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 14Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 15Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 16Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 17State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 18Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 19Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 20Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 21Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 22Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 23Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 24Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
IGCSE Question 25State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.

H. British Curriculum / A-Level Physics

A-Level Advanced 1State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 2Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 3Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 4Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 5Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 6Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 7Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 8Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 9State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 10Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 11Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 12Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 13Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 14Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 15Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 16Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 17State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 18Derive magnetic field inside a long solenoid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 19Derive magnetic field inside and outside a solid cylindrical conductor.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 20Derive magnetic field inside a toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 21Explain the B-r graph for a current-carrying cylinder.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 22Compare solenoid and toroid.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 23Explain why Ampere's Law requires symmetry for easy application.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 24Explain the direction of magnetic field using right-hand thumb rule.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.
A-Level Advanced 25State Ampere's Circuital Law and explain each term.
Solution: Use ∮B·dℓ = μ₀I_enclosed. Choose a symmetric Amperian path, identify the current enclosed, evaluate the line integral, and solve for B. Draw the required diagram and mention the valid region of the formula.

12. Case Study Section

Case Study 1solenoid as electromagnet
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 2MRI machine solenoid
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 3toroidal transformer
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 4current-carrying wire core
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 5B-r graph interpretation
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 6solenoid as electromagnet
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 7MRI machine solenoid
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 8toroidal transformer
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 9current-carrying wire core
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 10B-r graph interpretation
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 11solenoid as electromagnet
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 12MRI machine solenoid
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 13toroidal transformer
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 14current-carrying wire core
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 15B-r graph interpretation
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 16solenoid as electromagnet
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 17MRI machine solenoid
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 18toroidal transformer
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 19current-carrying wire core
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.
Case Study 20B-r graph interpretation
Scenario: A practical device uses current distribution with high symmetry. Data: current I, turns N, turns per unit length n, radius r or R are given. Questions: identify valid Amperian path, find I_enclosed, calculate B, and explain graph or direction. Solution: Apply ∮B·dℓ = μ₀I_enclosed. For solenoid use B=μ₀nI, for toroid use B=μ₀NI/2πr, and for cylinder use inside/outside formulas according to r<R or r>R.

13. Final Revision Sheet

Ampere's Law∮B·dℓ = μ₀I_enclosed
H-form∮H·dℓ = I_enclosed
Long wireB = μ₀I/2πr
Cylinder insideB = μ₀Ir/2πR²
Cylinder outsideB = μ₀I/2πr
SolenoidB = μ₀nI
Solenoid endB = μ₀nI/2
ToroidB = μ₀NI/2πr

Direction rule: Thumb gives current direction; curled fingers show magnetic field direction. NEET trap: use current enclosed. JEE trap: choose the correct Amperian path and valid region.

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