Magnetic Force and Motion of a Charged Particle in Magnetic Field
Moving Charges and Magnetism

Magnetic Force and Motion of a Charged Particle in Magnetic Field

Complete premium style Physics notes by Kumar Sir with vector diagrams, derivations, formula boxes, concept maps, MCQs, case studies and revision sheets for CBSE, NEET, IIT JEE, JEE Advanced, IB, AP, IGCSE, ICSE and British Curriculum Physics magnetic force and motion in magnetic field .

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1. Force Experienced by a Charged Particle Placed in a Magnetic Field

Vector Form

A magnetic field does not push every charge. It acts on a moving charge. For a positive charge, direction is given by the cross product of velocity and magnetic field.

F = q(v x B)

Magnitude:

F = qvB sin theta

If charge is negative, the force direction is opposite to v x B.

Vector Diagram: v, B, F and thetaBvFtheta+

v parallel B

theta=0 or 180 degrees, so sin theta=0 and F=0. Particle moves in a straight line.

v perpendicular B

theta=90 degrees, so F=qvB. Force is maximum and acts as centripetal force.

v at angle theta

Only v_perpendicular=v sin theta contributes to force. Motion becomes helical.

2. Lorentz Force

Lorentz force is the total force on a charged particle when electric and magnetic fields are present together.

F = q(E + v x B)

Only electric field: F=qE and force may change speed.
Only magnetic field: F=q(v x B) and speed remains constant.
Both fields: electric and magnetic forces combine vectorially.

Lorentz Force Vector AdditionqvBqEF totalF = q(E + v x B)

3. Unit and Dimension of Magnetic Field

Unit Derivation

From F=qvB
B=F/qv
B=N/(C m s^-1)
Since C=A s, B=N/(A m)
1 Tesla = 1 N A^-1 m^-1

Dimensional Formula

[F]=M L T^-2
[q]=A T and [v]=L T^-1
[B]=[F]/([q][v])
[B]=M T^-2 A^-1

Physical Meaning

A 1 tesla magnetic field is strong enough to exert 1 N force on a 1 A current-carrying conductor of length 1 m placed perpendicular to it.

4. Representation of Magnetic Field

Dots: Magnetic Field Coming OutDots mean B out of page
Crosses: Magnetic Field Going InxxxxxxxxxxxxxxxxxxxxxxxxCrosses mean B into page
Particle Entering Dot Fieldpositive charge curves clockwise/anticlockwise as per q
Particle Entering Cross Fieldxxxxxxxxxxxxxxxxxxpath bends opposite for reversed B or negative q

Dot means arrow tip coming towards observer. Cross means arrow tail going away from observer. Always mark dots/crosses clearly in board and competitive exam diagrams.

5. Fleming's Rules and Cross Product Direction

Fleming's Left Hand Rule

Used to find force on current-carrying conductor or moving positive charge. First finger gives magnetic field, second finger gives current/positive charge velocity, thumb gives force.

Fleming Left Hand RuleThumb: ForceSecond: CurrentFirst: Field

Fleming's Right Hand Rule

Used in electromagnetic induction. Thumb gives motion, first finger gives magnetic field, second finger gives induced current.

Fleming Right Hand RuleThumb: MotionSecond: Induced currentFirst: Field

6. Motion of Charged Particle in Magnetic Field

Case 1: Parallel Entry

theta=0, F=0. Particle moves straight.

Case 2: Perpendicular Entry

theta=90, F=qvB. Magnetic force acts as centripetal force.

Case 3: Oblique Entry

Resolve velocity into v_parallel and v_perpendicular. Motion becomes helical.

Straight Line MotionBv parallel B, F = 0
Circular MotionxxxxxxxxxxxxxxxxxxvF
Helical MotionpitchB and v_parallel
Velocity Componentsvv_parallel = v cos thetav_perp = v sin theta

7. Particle Accelerated Through Potential Difference

Velocity Derivation

Electrical work done = qV
This becomes kinetic energy.
qV = 1/2 mv^2
v = sqrt(2qV/m)

Specific Charge

Specific charge means charge-to-mass ratio of a particle.

q/m = v^2/(2V)

Connection with Circular Motion

Substitute v from acceleration into r=mv/qB to relate radius, field and potential.

8. Radius of Circular Path

Step-by-Step Derivation

Magnetic force provides centripetal force.
qvB = mv^2/r
Cancel v.
r = mv/qB
Using v=sqrt(2qV/m), r=sqrt(2mV/q)/B
Therefore q/m=2V/(B^2r^2)
Circular Path RadiusrvF to centre

9. Time Period, Frequency and Angular Frequency

Time Period

T=circumference/speed
T=2 pi r/v
Substitute r=mv/qB
T=2 pi m/qB

Frequency

f=qB/(2 pi m)

Angular Frequency

omega=qB/m

T, f and omega are independent of speed and radius.

10. Helical Motion

Formulae

v_perpendicular = v sin theta

v_parallel = v cos theta

r = mv sin theta/qBT = 2 pi m/qBp = v cos theta x 2 pi m/qB
3D Style Helical PathpitchB and v_parallel

11. Velocity Selector and Applications

Derivation

Electric force = qE
Magnetic force = qvB
For undeflected motion, qE=qvB
v=E/B

Applications: mass spectrometer, particle beam control and selection of particles of same speed.

Velocity Selector+-EvFBFEundeflected: v = E/B

12. Applications

Cyclotron

Magnetic force controls charged-particle path and helps measure, guide, accelerate or separate particles.

Mass Spectrometer

Magnetic force controls charged-particle path and helps measure, guide, accelerate or separate particles.

Velocity Selector

Magnetic force controls charged-particle path and helps measure, guide, accelerate or separate particles.

Electron Beam Tube

Magnetic force controls charged-particle path and helps measure, guide, accelerate or separate particles.

Particle Accelerator

Magnetic force controls charged-particle path and helps measure, guide, accelerate or separate particles.

Cathode Ray Tube

Magnetic force controls charged-particle path and helps measure, guide, accelerate or separate particles.

Medical Physics

Magnetic force controls charged-particle path and helps measure, guide, accelerate or separate particles.

Space Physics

Magnetic force controls charged-particle path and helps measure, guide, accelerate or separate particles.

Plasma Physics

Magnetic force controls charged-particle path and helps measure, guide, accelerate or separate particles.

13. Complete Exam Question Bank with Answers

CBSE Short Answer Questions

1State magnetic force on a moving charge.CBSE
Answer / Solution

A moving charge q with velocity v in magnetic field B experiences force F=q(v x B).

2Why is force zero when charge moves parallel to B?CBSE
Answer / Solution

Because theta is 0 or 180 degrees and sin theta is zero.

3What is Lorentz force?CBSE
Answer / Solution

The total force on a charge in electric and magnetic fields: F=q(E+v x B).

4What do dots and crosses represent?CBSE
Answer / Solution

Dots show B out of plane; crosses show B into plane.

5Why does magnetic force do no work?CBSE
Answer / Solution

It is always perpendicular to velocity, so F dot displacement is zero.

6Define one tesla.CBSE
Answer / Solution

One tesla is magnetic field that exerts 1 N force on 1 A m conductor perpendicular to field.

7What is velocity selector?CBSE
Answer / Solution

Crossed E and B field arrangement that allows only speed v=E/B to pass undeflected.

8What is pitch of helix?CBSE
Answer / Solution

Distance travelled parallel to magnetic field in one complete revolution.

9What is specific charge?CBSE
Answer / Solution

Charge-to-mass ratio q/m of a particle.

10What is cyclotron frequency?CBSE
Answer / Solution

Frequency of circular motion f=qB/(2 pi m).

11State magnetic force on a moving charge.CBSE
Answer / Solution

A moving charge q with velocity v in magnetic field B experiences force F=q(v x B).

12Why is force zero when charge moves parallel to B?CBSE
Answer / Solution

Because theta is 0 or 180 degrees and sin theta is zero.

13What is Lorentz force?CBSE
Answer / Solution

The total force on a charge in electric and magnetic fields: F=q(E+v x B).

14What do dots and crosses represent?CBSE
Answer / Solution

Dots show B out of plane; crosses show B into plane.

15Why does magnetic force do no work?CBSE
Answer / Solution

It is always perpendicular to velocity, so F dot displacement is zero.

16Define one tesla.CBSE
Answer / Solution

One tesla is magnetic field that exerts 1 N force on 1 A m conductor perpendicular to field.

17What is velocity selector?CBSE
Answer / Solution

Crossed E and B field arrangement that allows only speed v=E/B to pass undeflected.

18What is pitch of helix?CBSE
Answer / Solution

Distance travelled parallel to magnetic field in one complete revolution.

19What is specific charge?CBSE
Answer / Solution

Charge-to-mass ratio q/m of a particle.

20What is cyclotron frequency?CBSE
Answer / Solution

Frequency of circular motion f=qB/(2 pi m).

CBSE Derivation Questions

1Derive radius of circular path.CBSE Derivation
Answer / Solution

Use qvB=mv^2/r, hence r=mv/qB.

2Derive time period.CBSE Derivation
Answer / Solution

T=2 pi r/v; substitute r=mv/qB to get T=2 pi m/qB.

3Derive frequency.CBSE Derivation
Answer / Solution

f=1/T=qB/(2 pi m).

4Derive angular frequency.CBSE Derivation
Answer / Solution

omega=2 pi f=qB/m.

5Derive velocity selector formula.CBSE Derivation
Answer / Solution

For undeflected path qE=qvB, so v=E/B.

6Derive speed after acceleration through potential V.CBSE Derivation
Answer / Solution

qV=1/2 mv^2, so v=sqrt(2qV/m).

7Derive specific charge expression.CBSE Derivation
Answer / Solution

Combine r=mv/qB and qV=1/2mv^2 to get q/m=2V/(B^2r^2).

8Derive pitch of helix.CBSE Derivation
Answer / Solution

Pitch=p=v_parallel T=v cos theta x 2 pi m/qB.

9Derive radius of circular path.CBSE Derivation
Answer / Solution

Use qvB=mv^2/r, hence r=mv/qB.

10Derive time period.CBSE Derivation
Answer / Solution

T=2 pi r/v; substitute r=mv/qB to get T=2 pi m/qB.

11Derive frequency.CBSE Derivation
Answer / Solution

f=1/T=qB/(2 pi m).

12Derive angular frequency.CBSE Derivation
Answer / Solution

omega=2 pi f=qB/m.

13Derive velocity selector formula.CBSE Derivation
Answer / Solution

For undeflected path qE=qvB, so v=E/B.

14Derive speed after acceleration through potential V.CBSE Derivation
Answer / Solution

qV=1/2 mv^2, so v=sqrt(2qV/m).

15Derive specific charge expression.CBSE Derivation
Answer / Solution

Combine r=mv/qB and qV=1/2mv^2 to get q/m=2V/(B^2r^2).

16Derive pitch of helix.CBSE Derivation
Answer / Solution

Pitch=p=v_parallel T=v cos theta x 2 pi m/qB.

17Derive radius of circular path.CBSE Derivation
Answer / Solution

Use qvB=mv^2/r, hence r=mv/qB.

18Derive time period.CBSE Derivation
Answer / Solution

T=2 pi r/v; substitute r=mv/qB to get T=2 pi m/qB.

19Derive frequency.CBSE Derivation
Answer / Solution

f=1/T=qB/(2 pi m).

20Derive angular frequency.CBSE Derivation
Answer / Solution

omega=2 pi f=qB/m.

CBSE Numerical Questions

1A proton of speed 2 x 10^6 m/s enters B=0.5 T perpendicularly. Find radius. Take m/q=1.04 x 10^-8 kg/C.CBSE Numerical
Answer / Solution

r=mv/qB=(m/q)v/B=1.04e-8 x 2e6/0.5=0.0416 m.

2In a velocity selector E=4 x 10^4 V/m and B=0.2 T. Find selected speed.CBSE Numerical
Answer / Solution

v=E/B=2 x 10^5 m/s.

3A particle has q/m=5 x 10^7 C/kg and moves in B=0.1 T. Find angular frequency.CBSE Numerical
Answer / Solution

omega=qB/m=(q/m)B=5 x 10^6 rad/s.

4If speed is doubled in same B, what happens to radius?CBSE Numerical
Answer / Solution

Radius doubles because r is proportional to v.

5If B is doubled, what happens to time period?CBSE Numerical
Answer / Solution

T becomes half because T is inversely proportional to B.

6An electron accelerated by V enters B perpendicular. Which formula gives q/m?CBSE Numerical
Answer / Solution

q/m=2V/(B^2r^2).

7A proton of speed 2 x 10^6 m/s enters B=0.5 T perpendicularly. Find radius. Take m/q=1.04 x 10^-8 kg/C.CBSE Numerical
Answer / Solution

r=mv/qB=(m/q)v/B=1.04e-8 x 2e6/0.5=0.0416 m.

8In a velocity selector E=4 x 10^4 V/m and B=0.2 T. Find selected speed.CBSE Numerical
Answer / Solution

v=E/B=2 x 10^5 m/s.

9A particle has q/m=5 x 10^7 C/kg and moves in B=0.1 T. Find angular frequency.CBSE Numerical
Answer / Solution

omega=qB/m=(q/m)B=5 x 10^6 rad/s.

10If speed is doubled in same B, what happens to radius?CBSE Numerical
Answer / Solution

Radius doubles because r is proportional to v.

11If B is doubled, what happens to time period?CBSE Numerical
Answer / Solution

T becomes half because T is inversely proportional to B.

12An electron accelerated by V enters B perpendicular. Which formula gives q/m?CBSE Numerical
Answer / Solution

q/m=2V/(B^2r^2).

13A proton of speed 2 x 10^6 m/s enters B=0.5 T perpendicularly. Find radius. Take m/q=1.04 x 10^-8 kg/C.CBSE Numerical
Answer / Solution

r=mv/qB=(m/q)v/B=1.04e-8 x 2e6/0.5=0.0416 m.

14In a velocity selector E=4 x 10^4 V/m and B=0.2 T. Find selected speed.CBSE Numerical
Answer / Solution

v=E/B=2 x 10^5 m/s.

15A particle has q/m=5 x 10^7 C/kg and moves in B=0.1 T. Find angular frequency.CBSE Numerical
Answer / Solution

omega=qB/m=(q/m)B=5 x 10^6 rad/s.

16If speed is doubled in same B, what happens to radius?CBSE Numerical
Answer / Solution

Radius doubles because r is proportional to v.

17If B is doubled, what happens to time period?CBSE Numerical
Answer / Solution

T becomes half because T is inversely proportional to B.

18An electron accelerated by V enters B perpendicular. Which formula gives q/m?CBSE Numerical
Answer / Solution

q/m=2V/(B^2r^2).

19A proton of speed 2 x 10^6 m/s enters B=0.5 T perpendicularly. Find radius. Take m/q=1.04 x 10^-8 kg/C.CBSE Numerical
Answer / Solution

r=mv/qB=(m/q)v/B=1.04e-8 x 2e6/0.5=0.0416 m.

20In a velocity selector E=4 x 10^4 V/m and B=0.2 T. Find selected speed.CBSE Numerical
Answer / Solution

v=E/B=2 x 10^5 m/s.

Case Study Questions

1Cyclotron CaseCase Study
Answer / Solution

A charged particle rotates in a cyclotron under uniform magnetic field. Explain why frequency is nearly constant and why radius increases.

2Mass Spectrometer CaseCase Study
Answer / Solution

Ions accelerated through same potential enter same magnetic field and form different radii.

3Velocity Selector CaseCase Study
Answer / Solution

A beam passes through crossed electric and magnetic fields and only one speed goes undeflected.

4Electron Beam CaseCase Study
Answer / Solution

Electron beam bends in a magnetic field in a cathode ray tube.

5Space Physics CaseCase Study
Answer / Solution

Charged particles spiral around Earth's magnetic field lines.

6Cyclotron CaseCase Study
Answer / Solution

A charged particle rotates in a cyclotron under uniform magnetic field. Explain why frequency is nearly constant and why radius increases.

7Mass Spectrometer CaseCase Study
Answer / Solution

Ions accelerated through same potential enter same magnetic field and form different radii.

8Velocity Selector CaseCase Study
Answer / Solution

A beam passes through crossed electric and magnetic fields and only one speed goes undeflected.

9Electron Beam CaseCase Study
Answer / Solution

Electron beam bends in a magnetic field in a cathode ray tube.

10Space Physics CaseCase Study
Answer / Solution

Charged particles spiral around Earth's magnetic field lines.

NEET Tough MCQs

1Magnetic force is maximum when angle between v and B isNEET
A) 0 degree
B) 45 degree
C) 90 degree
D) 180 degree
Correct Answer and Explanation

Answer: C. F=qvB sin theta is maximum at 90 degree.

2A charged particle moves parallel to uniform B. Its path isNEET
A) circle
B) helix
C) straight line
D) parabola
Correct Answer and Explanation

Answer: C. F=0 for parallel motion.

3A proton and electron have same speed in same B. Larger radius belongs toNEET
A) electron
B) proton
C) same
D) cannot say
Correct Answer and Explanation

Answer: B. r=mv/qB; proton mass is larger.

4Magnetic force does work equal toNEET
A) qvB
B) qVB
C) zero
D) mv^2/r
Correct Answer and Explanation

Answer: C. Force is perpendicular to displacement.

5Velocity selected by crossed fields isNEET
A) EB
B) B/E
C) E/B
D) qE/B
Correct Answer and Explanation

Answer: C. qE=qvB gives v=E/B.

6Cyclotron frequency depends onNEET
A) speed
B) radius
C) q/m and B
D) kinetic energy
Correct Answer and Explanation

Answer: C. f=qB/2pi m.

7For negative charge, force direction isNEET
A) same as v x B
B) opposite to v x B
C) always zero
D) along B
Correct Answer and Explanation

Answer: B. q is negative, so direction reverses.

8Unit tesla is equal toNEET
A) N A m
B) N A^-1 m^-1
C) N C m^-1
D) J A^-1
Correct Answer and Explanation

Answer: B. B=F/(IL), so tesla=N/(A m).

9Dimension of B isNEET
A) M T^-2 A^-1
B) M L T^-2
C) M L^2 T^-2
D) A T^-1
Correct Answer and Explanation

Answer: A. From B=F/(qv), [B]=M T^-2 A^-1.

10In helical motion, radius depends onNEET
A) v parallel
B) v perpendicular
C) total speed only
D) pitch only
Correct Answer and Explanation

Answer: B. r=mv_perp/qB.

11Magnetic force is maximum when angle between v and B isNEET
A) 0 degree
B) 45 degree
C) 90 degree
D) 180 degree
Correct Answer and Explanation

Answer: C. F=qvB sin theta is maximum at 90 degree.

12A charged particle moves parallel to uniform B. Its path isNEET
A) circle
B) helix
C) straight line
D) parabola
Correct Answer and Explanation

Answer: C. F=0 for parallel motion.

13A proton and electron have same speed in same B. Larger radius belongs toNEET
A) electron
B) proton
C) same
D) cannot say
Correct Answer and Explanation

Answer: B. r=mv/qB; proton mass is larger.

14Magnetic force does work equal toNEET
A) qvB
B) qVB
C) zero
D) mv^2/r
Correct Answer and Explanation

Answer: C. Force is perpendicular to displacement.

15Velocity selected by crossed fields isNEET
A) EB
B) B/E
C) E/B
D) qE/B
Correct Answer and Explanation

Answer: C. qE=qvB gives v=E/B.

16Cyclotron frequency depends onNEET
A) speed
B) radius
C) q/m and B
D) kinetic energy
Correct Answer and Explanation

Answer: C. f=qB/2pi m.

17For negative charge, force direction isNEET
A) same as v x B
B) opposite to v x B
C) always zero
D) along B
Correct Answer and Explanation

Answer: B. q is negative, so direction reverses.

18Unit tesla is equal toNEET
A) N A m
B) N A^-1 m^-1
C) N C m^-1
D) J A^-1
Correct Answer and Explanation

Answer: B. B=F/(IL), so tesla=N/(A m).

19Dimension of B isNEET
A) M T^-2 A^-1
B) M L T^-2
C) M L^2 T^-2
D) A T^-1
Correct Answer and Explanation

Answer: A. From B=F/(qv), [B]=M T^-2 A^-1.

20In helical motion, radius depends onNEET
A) v parallel
B) v perpendicular
C) total speed only
D) pitch only
Correct Answer and Explanation

Answer: B. r=mv_perp/qB.

21Magnetic force is maximum when angle between v and B isNEET
A) 0 degree
B) 45 degree
C) 90 degree
D) 180 degree
Correct Answer and Explanation

Answer: C. F=qvB sin theta is maximum at 90 degree.

22A charged particle moves parallel to uniform B. Its path isNEET
A) circle
B) helix
C) straight line
D) parabola
Correct Answer and Explanation

Answer: C. F=0 for parallel motion.

23A proton and electron have same speed in same B. Larger radius belongs toNEET
A) electron
B) proton
C) same
D) cannot say
Correct Answer and Explanation

Answer: B. r=mv/qB; proton mass is larger.

24Magnetic force does work equal toNEET
A) qvB
B) qVB
C) zero
D) mv^2/r
Correct Answer and Explanation

Answer: C. Force is perpendicular to displacement.

25Velocity selected by crossed fields isNEET
A) EB
B) B/E
C) E/B
D) qE/B
Correct Answer and Explanation

Answer: C. qE=qvB gives v=E/B.

26Cyclotron frequency depends onNEET
A) speed
B) radius
C) q/m and B
D) kinetic energy
Correct Answer and Explanation

Answer: C. f=qB/2pi m.

27For negative charge, force direction isNEET
A) same as v x B
B) opposite to v x B
C) always zero
D) along B
Correct Answer and Explanation

Answer: B. q is negative, so direction reverses.

28Unit tesla is equal toNEET
A) N A m
B) N A^-1 m^-1
C) N C m^-1
D) J A^-1
Correct Answer and Explanation

Answer: B. B=F/(IL), so tesla=N/(A m).

29Dimension of B isNEET
A) M T^-2 A^-1
B) M L T^-2
C) M L^2 T^-2
D) A T^-1
Correct Answer and Explanation

Answer: A. From B=F/(qv), [B]=M T^-2 A^-1.

30In helical motion, radius depends onNEET
A) v parallel
B) v perpendicular
C) total speed only
D) pitch only
Correct Answer and Explanation

Answer: B. r=mv_perp/qB.

31Magnetic force is maximum when angle between v and B isNEET
A) 0 degree
B) 45 degree
C) 90 degree
D) 180 degree
Correct Answer and Explanation

Answer: C. F=qvB sin theta is maximum at 90 degree.

32A charged particle moves parallel to uniform B. Its path isNEET
A) circle
B) helix
C) straight line
D) parabola
Correct Answer and Explanation

Answer: C. F=0 for parallel motion.

33A proton and electron have same speed in same B. Larger radius belongs toNEET
A) electron
B) proton
C) same
D) cannot say
Correct Answer and Explanation

Answer: B. r=mv/qB; proton mass is larger.

34Magnetic force does work equal toNEET
A) qvB
B) qVB
C) zero
D) mv^2/r
Correct Answer and Explanation

Answer: C. Force is perpendicular to displacement.

35Velocity selected by crossed fields isNEET
A) EB
B) B/E
C) E/B
D) qE/B
Correct Answer and Explanation

Answer: C. qE=qvB gives v=E/B.

36Cyclotron frequency depends onNEET
A) speed
B) radius
C) q/m and B
D) kinetic energy
Correct Answer and Explanation

Answer: C. f=qB/2pi m.

37For negative charge, force direction isNEET
A) same as v x B
B) opposite to v x B
C) always zero
D) along B
Correct Answer and Explanation

Answer: B. q is negative, so direction reverses.

38Unit tesla is equal toNEET
A) N A m
B) N A^-1 m^-1
C) N C m^-1
D) J A^-1
Correct Answer and Explanation

Answer: B. B=F/(IL), so tesla=N/(A m).

39Dimension of B isNEET
A) M T^-2 A^-1
B) M L T^-2
C) M L^2 T^-2
D) A T^-1
Correct Answer and Explanation

Answer: A. From B=F/(qv), [B]=M T^-2 A^-1.

40In helical motion, radius depends onNEET
A) v parallel
B) v perpendicular
C) total speed only
D) pitch only
Correct Answer and Explanation

Answer: B. r=mv_perp/qB.

41Magnetic force is maximum when angle between v and B isNEET
A) 0 degree
B) 45 degree
C) 90 degree
D) 180 degree
Correct Answer and Explanation

Answer: C. F=qvB sin theta is maximum at 90 degree.

42A charged particle moves parallel to uniform B. Its path isNEET
A) circle
B) helix
C) straight line
D) parabola
Correct Answer and Explanation

Answer: C. F=0 for parallel motion.

43A proton and electron have same speed in same B. Larger radius belongs toNEET
A) electron
B) proton
C) same
D) cannot say
Correct Answer and Explanation

Answer: B. r=mv/qB; proton mass is larger.

44Magnetic force does work equal toNEET
A) qvB
B) qVB
C) zero
D) mv^2/r
Correct Answer and Explanation

Answer: C. Force is perpendicular to displacement.

45Velocity selected by crossed fields isNEET
A) EB
B) B/E
C) E/B
D) qE/B
Correct Answer and Explanation

Answer: C. qE=qvB gives v=E/B.

46Cyclotron frequency depends onNEET
A) speed
B) radius
C) q/m and B
D) kinetic energy
Correct Answer and Explanation

Answer: C. f=qB/2pi m.

47For negative charge, force direction isNEET
A) same as v x B
B) opposite to v x B
C) always zero
D) along B
Correct Answer and Explanation

Answer: B. q is negative, so direction reverses.

48Unit tesla is equal toNEET
A) N A m
B) N A^-1 m^-1
C) N C m^-1
D) J A^-1
Correct Answer and Explanation

Answer: B. B=F/(IL), so tesla=N/(A m).

49Dimension of B isNEET
A) M T^-2 A^-1
B) M L T^-2
C) M L^2 T^-2
D) A T^-1
Correct Answer and Explanation

Answer: A. From B=F/(qv), [B]=M T^-2 A^-1.

50In helical motion, radius depends onNEET
A) v parallel
B) v perpendicular
C) total speed only
D) pitch only
Correct Answer and Explanation

Answer: B. r=mv_perp/qB.

51Magnetic force is maximum when angle between v and B isNEET
A) 0 degree
B) 45 degree
C) 90 degree
D) 180 degree
Correct Answer and Explanation

Answer: C. F=qvB sin theta is maximum at 90 degree.

52A charged particle moves parallel to uniform B. Its path isNEET
A) circle
B) helix
C) straight line
D) parabola
Correct Answer and Explanation

Answer: C. F=0 for parallel motion.

53A proton and electron have same speed in same B. Larger radius belongs toNEET
A) electron
B) proton
C) same
D) cannot say
Correct Answer and Explanation

Answer: B. r=mv/qB; proton mass is larger.

54Magnetic force does work equal toNEET
A) qvB
B) qVB
C) zero
D) mv^2/r
Correct Answer and Explanation

Answer: C. Force is perpendicular to displacement.

55Velocity selected by crossed fields isNEET
A) EB
B) B/E
C) E/B
D) qE/B
Correct Answer and Explanation

Answer: C. qE=qvB gives v=E/B.

56Cyclotron frequency depends onNEET
A) speed
B) radius
C) q/m and B
D) kinetic energy
Correct Answer and Explanation

Answer: C. f=qB/2pi m.

57For negative charge, force direction isNEET
A) same as v x B
B) opposite to v x B
C) always zero
D) along B
Correct Answer and Explanation

Answer: B. q is negative, so direction reverses.

58Unit tesla is equal toNEET
A) N A m
B) N A^-1 m^-1
C) N C m^-1
D) J A^-1
Correct Answer and Explanation

Answer: B. B=F/(IL), so tesla=N/(A m).

59Dimension of B isNEET
A) M T^-2 A^-1
B) M L T^-2
C) M L^2 T^-2
D) A T^-1
Correct Answer and Explanation

Answer: A. From B=F/(qv), [B]=M T^-2 A^-1.

60In helical motion, radius depends onNEET
A) v parallel
B) v perpendicular
C) total speed only
D) pitch only
Correct Answer and Explanation

Answer: B. r=mv_perp/qB.

61Magnetic force is maximum when angle between v and B isNEET
A) 0 degree
B) 45 degree
C) 90 degree
D) 180 degree
Correct Answer and Explanation

Answer: C. F=qvB sin theta is maximum at 90 degree.

62A charged particle moves parallel to uniform B. Its path isNEET
A) circle
B) helix
C) straight line
D) parabola
Correct Answer and Explanation

Answer: C. F=0 for parallel motion.

63A proton and electron have same speed in same B. Larger radius belongs toNEET
A) electron
B) proton
C) same
D) cannot say
Correct Answer and Explanation

Answer: B. r=mv/qB; proton mass is larger.

64Magnetic force does work equal toNEET
A) qvB
B) qVB
C) zero
D) mv^2/r
Correct Answer and Explanation

Answer: C. Force is perpendicular to displacement.

65Velocity selected by crossed fields isNEET
A) EB
B) B/E
C) E/B
D) qE/B
Correct Answer and Explanation

Answer: C. qE=qvB gives v=E/B.

66Cyclotron frequency depends onNEET
A) speed
B) radius
C) q/m and B
D) kinetic energy
Correct Answer and Explanation

Answer: C. f=qB/2pi m.

67For negative charge, force direction isNEET
A) same as v x B
B) opposite to v x B
C) always zero
D) along B
Correct Answer and Explanation

Answer: B. q is negative, so direction reverses.

68Unit tesla is equal toNEET
A) N A m
B) N A^-1 m^-1
C) N C m^-1
D) J A^-1
Correct Answer and Explanation

Answer: B. B=F/(IL), so tesla=N/(A m).

69Dimension of B isNEET
A) M T^-2 A^-1
B) M L T^-2
C) M L^2 T^-2
D) A T^-1
Correct Answer and Explanation

Answer: A. From B=F/(qv), [B]=M T^-2 A^-1.

70In helical motion, radius depends onNEET
A) v parallel
B) v perpendicular
C) total speed only
D) pitch only
Correct Answer and Explanation

Answer: B. r=mv_perp/qB.

71Magnetic force is maximum when angle between v and B isNEET
A) 0 degree
B) 45 degree
C) 90 degree
D) 180 degree
Correct Answer and Explanation

Answer: C. F=qvB sin theta is maximum at 90 degree.

72A charged particle moves parallel to uniform B. Its path isNEET
A) circle
B) helix
C) straight line
D) parabola
Correct Answer and Explanation

Answer: C. F=0 for parallel motion.

73A proton and electron have same speed in same B. Larger radius belongs toNEET
A) electron
B) proton
C) same
D) cannot say
Correct Answer and Explanation

Answer: B. r=mv/qB; proton mass is larger.

74Magnetic force does work equal toNEET
A) qvB
B) qVB
C) zero
D) mv^2/r
Correct Answer and Explanation

Answer: C. Force is perpendicular to displacement.

75Velocity selected by crossed fields isNEET
A) EB
B) B/E
C) E/B
D) qE/B
Correct Answer and Explanation

Answer: C. qE=qvB gives v=E/B.

JEE Main MCQs

1Magnetic force is maximum when angle between v and B isJEE Main
A) 0 degree
B) 45 degree
C) 90 degree
D) 180 degree
Correct Answer and Explanation

Answer: C. F=qvB sin theta is maximum at 90 degree.

2A charged particle moves parallel to uniform B. Its path isJEE Main
A) circle
B) helix
C) straight line
D) parabola
Correct Answer and Explanation

Answer: C. F=0 for parallel motion.

3A proton and electron have same speed in same B. Larger radius belongs toJEE Main
A) electron
B) proton
C) same
D) cannot say
Correct Answer and Explanation

Answer: B. r=mv/qB; proton mass is larger.

4Magnetic force does work equal toJEE Main
A) qvB
B) qVB
C) zero
D) mv^2/r
Correct Answer and Explanation

Answer: C. Force is perpendicular to displacement.

5Velocity selected by crossed fields isJEE Main
A) EB
B) B/E
C) E/B
D) qE/B
Correct Answer and Explanation

Answer: C. qE=qvB gives v=E/B.

6Cyclotron frequency depends onJEE Main
A) speed
B) radius
C) q/m and B
D) kinetic energy
Correct Answer and Explanation

Answer: C. f=qB/2pi m.

7For negative charge, force direction isJEE Main
A) same as v x B
B) opposite to v x B
C) always zero
D) along B
Correct Answer and Explanation

Answer: B. q is negative, so direction reverses.

8Unit tesla is equal toJEE Main
A) N A m
B) N A^-1 m^-1
C) N C m^-1
D) J A^-1
Correct Answer and Explanation

Answer: B. B=F/(IL), so tesla=N/(A m).

9Dimension of B isJEE Main
A) M T^-2 A^-1
B) M L T^-2
C) M L^2 T^-2
D) A T^-1
Correct Answer and Explanation

Answer: A. From B=F/(qv), [B]=M T^-2 A^-1.

10In helical motion, radius depends onJEE Main
A) v parallel
B) v perpendicular
C) total speed only
D) pitch only
Correct Answer and Explanation

Answer: B. r=mv_perp/qB.

11A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?JEE Main
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

12A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesJEE Main
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

13Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isJEE Main
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

14Multiple correct: In pure magnetic fieldJEE Main
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

15Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isJEE Main
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

16Magnetic force is maximum when angle between v and B isJEE Main
A) 0 degree
B) 45 degree
C) 90 degree
D) 180 degree
Correct Answer and Explanation

Answer: C. F=qvB sin theta is maximum at 90 degree.

17A charged particle moves parallel to uniform B. Its path isJEE Main
A) circle
B) helix
C) straight line
D) parabola
Correct Answer and Explanation

Answer: C. F=0 for parallel motion.

18A proton and electron have same speed in same B. Larger radius belongs toJEE Main
A) electron
B) proton
C) same
D) cannot say
Correct Answer and Explanation

Answer: B. r=mv/qB; proton mass is larger.

19Magnetic force does work equal toJEE Main
A) qvB
B) qVB
C) zero
D) mv^2/r
Correct Answer and Explanation

Answer: C. Force is perpendicular to displacement.

20Velocity selected by crossed fields isJEE Main
A) EB
B) B/E
C) E/B
D) qE/B
Correct Answer and Explanation

Answer: C. qE=qvB gives v=E/B.

21Cyclotron frequency depends onJEE Main
A) speed
B) radius
C) q/m and B
D) kinetic energy
Correct Answer and Explanation

Answer: C. f=qB/2pi m.

22For negative charge, force direction isJEE Main
A) same as v x B
B) opposite to v x B
C) always zero
D) along B
Correct Answer and Explanation

Answer: B. q is negative, so direction reverses.

23Unit tesla is equal toJEE Main
A) N A m
B) N A^-1 m^-1
C) N C m^-1
D) J A^-1
Correct Answer and Explanation

Answer: B. B=F/(IL), so tesla=N/(A m).

24Dimension of B isJEE Main
A) M T^-2 A^-1
B) M L T^-2
C) M L^2 T^-2
D) A T^-1
Correct Answer and Explanation

Answer: A. From B=F/(qv), [B]=M T^-2 A^-1.

25In helical motion, radius depends onJEE Main
A) v parallel
B) v perpendicular
C) total speed only
D) pitch only
Correct Answer and Explanation

Answer: B. r=mv_perp/qB.

26A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?JEE Main
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

27A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesJEE Main
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

28Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isJEE Main
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

29Multiple correct: In pure magnetic fieldJEE Main
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

30Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isJEE Main
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

31Magnetic force is maximum when angle between v and B isJEE Main
A) 0 degree
B) 45 degree
C) 90 degree
D) 180 degree
Correct Answer and Explanation

Answer: C. F=qvB sin theta is maximum at 90 degree.

32A charged particle moves parallel to uniform B. Its path isJEE Main
A) circle
B) helix
C) straight line
D) parabola
Correct Answer and Explanation

Answer: C. F=0 for parallel motion.

33A proton and electron have same speed in same B. Larger radius belongs toJEE Main
A) electron
B) proton
C) same
D) cannot say
Correct Answer and Explanation

Answer: B. r=mv/qB; proton mass is larger.

34Magnetic force does work equal toJEE Main
A) qvB
B) qVB
C) zero
D) mv^2/r
Correct Answer and Explanation

Answer: C. Force is perpendicular to displacement.

35Velocity selected by crossed fields isJEE Main
A) EB
B) B/E
C) E/B
D) qE/B
Correct Answer and Explanation

Answer: C. qE=qvB gives v=E/B.

36Cyclotron frequency depends onJEE Main
A) speed
B) radius
C) q/m and B
D) kinetic energy
Correct Answer and Explanation

Answer: C. f=qB/2pi m.

37For negative charge, force direction isJEE Main
A) same as v x B
B) opposite to v x B
C) always zero
D) along B
Correct Answer and Explanation

Answer: B. q is negative, so direction reverses.

38Unit tesla is equal toJEE Main
A) N A m
B) N A^-1 m^-1
C) N C m^-1
D) J A^-1
Correct Answer and Explanation

Answer: B. B=F/(IL), so tesla=N/(A m).

39Dimension of B isJEE Main
A) M T^-2 A^-1
B) M L T^-2
C) M L^2 T^-2
D) A T^-1
Correct Answer and Explanation

Answer: A. From B=F/(qv), [B]=M T^-2 A^-1.

40In helical motion, radius depends onJEE Main
A) v parallel
B) v perpendicular
C) total speed only
D) pitch only
Correct Answer and Explanation

Answer: B. r=mv_perp/qB.

41A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?JEE Main
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

42A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesJEE Main
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

43Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isJEE Main
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

44Multiple correct: In pure magnetic fieldJEE Main
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

45Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isJEE Main
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

46Magnetic force is maximum when angle between v and B isJEE Main
A) 0 degree
B) 45 degree
C) 90 degree
D) 180 degree
Correct Answer and Explanation

Answer: C. F=qvB sin theta is maximum at 90 degree.

47A charged particle moves parallel to uniform B. Its path isJEE Main
A) circle
B) helix
C) straight line
D) parabola
Correct Answer and Explanation

Answer: C. F=0 for parallel motion.

48A proton and electron have same speed in same B. Larger radius belongs toJEE Main
A) electron
B) proton
C) same
D) cannot say
Correct Answer and Explanation

Answer: B. r=mv/qB; proton mass is larger.

49Magnetic force does work equal toJEE Main
A) qvB
B) qVB
C) zero
D) mv^2/r
Correct Answer and Explanation

Answer: C. Force is perpendicular to displacement.

50Velocity selected by crossed fields isJEE Main
A) EB
B) B/E
C) E/B
D) qE/B
Correct Answer and Explanation

Answer: C. qE=qvB gives v=E/B.

51Cyclotron frequency depends onJEE Main
A) speed
B) radius
C) q/m and B
D) kinetic energy
Correct Answer and Explanation

Answer: C. f=qB/2pi m.

52For negative charge, force direction isJEE Main
A) same as v x B
B) opposite to v x B
C) always zero
D) along B
Correct Answer and Explanation

Answer: B. q is negative, so direction reverses.

53Unit tesla is equal toJEE Main
A) N A m
B) N A^-1 m^-1
C) N C m^-1
D) J A^-1
Correct Answer and Explanation

Answer: B. B=F/(IL), so tesla=N/(A m).

54Dimension of B isJEE Main
A) M T^-2 A^-1
B) M L T^-2
C) M L^2 T^-2
D) A T^-1
Correct Answer and Explanation

Answer: A. From B=F/(qv), [B]=M T^-2 A^-1.

55In helical motion, radius depends onJEE Main
A) v parallel
B) v perpendicular
C) total speed only
D) pitch only
Correct Answer and Explanation

Answer: B. r=mv_perp/qB.

56A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?JEE Main
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

57A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesJEE Main
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

58Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isJEE Main
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

59Multiple correct: In pure magnetic fieldJEE Main
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

60Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isJEE Main
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

61Magnetic force is maximum when angle between v and B isJEE Main
A) 0 degree
B) 45 degree
C) 90 degree
D) 180 degree
Correct Answer and Explanation

Answer: C. F=qvB sin theta is maximum at 90 degree.

62A charged particle moves parallel to uniform B. Its path isJEE Main
A) circle
B) helix
C) straight line
D) parabola
Correct Answer and Explanation

Answer: C. F=0 for parallel motion.

63A proton and electron have same speed in same B. Larger radius belongs toJEE Main
A) electron
B) proton
C) same
D) cannot say
Correct Answer and Explanation

Answer: B. r=mv/qB; proton mass is larger.

64Magnetic force does work equal toJEE Main
A) qvB
B) qVB
C) zero
D) mv^2/r
Correct Answer and Explanation

Answer: C. Force is perpendicular to displacement.

65Velocity selected by crossed fields isJEE Main
A) EB
B) B/E
C) E/B
D) qE/B
Correct Answer and Explanation

Answer: C. qE=qvB gives v=E/B.

66Cyclotron frequency depends onJEE Main
A) speed
B) radius
C) q/m and B
D) kinetic energy
Correct Answer and Explanation

Answer: C. f=qB/2pi m.

67For negative charge, force direction isJEE Main
A) same as v x B
B) opposite to v x B
C) always zero
D) along B
Correct Answer and Explanation

Answer: B. q is negative, so direction reverses.

68Unit tesla is equal toJEE Main
A) N A m
B) N A^-1 m^-1
C) N C m^-1
D) J A^-1
Correct Answer and Explanation

Answer: B. B=F/(IL), so tesla=N/(A m).

69Dimension of B isJEE Main
A) M T^-2 A^-1
B) M L T^-2
C) M L^2 T^-2
D) A T^-1
Correct Answer and Explanation

Answer: A. From B=F/(qv), [B]=M T^-2 A^-1.

70In helical motion, radius depends onJEE Main
A) v parallel
B) v perpendicular
C) total speed only
D) pitch only
Correct Answer and Explanation

Answer: B. r=mv_perp/qB.

71A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?JEE Main
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

72A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesJEE Main
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

73Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isJEE Main
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

74Multiple correct: In pure magnetic fieldJEE Main
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

75Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isJEE Main
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

JEE Advanced Single Correct

1A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?JEE Advanced
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

2A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesJEE Advanced
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

3Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isJEE Advanced
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

4Multiple correct: In pure magnetic fieldJEE Advanced
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

5Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isJEE Advanced
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

6A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?JEE Advanced
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

7A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesJEE Advanced
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

8Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isJEE Advanced
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

9Multiple correct: In pure magnetic fieldJEE Advanced
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

10Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isJEE Advanced
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

11A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?JEE Advanced
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

12A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesJEE Advanced
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

13Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isJEE Advanced
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

14Multiple correct: In pure magnetic fieldJEE Advanced
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

15Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isJEE Advanced
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

16A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?JEE Advanced
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

17A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesJEE Advanced
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

18Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isJEE Advanced
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

19Multiple correct: In pure magnetic fieldJEE Advanced
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

20Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isJEE Advanced
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

21A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?JEE Advanced
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

22A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesJEE Advanced
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

23Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isJEE Advanced
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

24Multiple correct: In pure magnetic fieldJEE Advanced
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

25Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isJEE Advanced
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

26A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?JEE Advanced
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

27A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesJEE Advanced
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

28Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isJEE Advanced
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

29Multiple correct: In pure magnetic fieldJEE Advanced
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

30Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isJEE Advanced
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

JEE Advanced Multiple Correct

1A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?Multiple Correct
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

2A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesMultiple Correct
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

3Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isMultiple Correct
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

4Multiple correct: In pure magnetic fieldMultiple Correct
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

5Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isMultiple Correct
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

6A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?Multiple Correct
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

7A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesMultiple Correct
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

8Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isMultiple Correct
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

9Multiple correct: In pure magnetic fieldMultiple Correct
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

10Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isMultiple Correct
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

11A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?Multiple Correct
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

12A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesMultiple Correct
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

13Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isMultiple Correct
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

14Multiple correct: In pure magnetic fieldMultiple Correct
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

15Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isMultiple Correct
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

16A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?Multiple Correct
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

17A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesMultiple Correct
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

18Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isMultiple Correct
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

19Multiple correct: In pure magnetic fieldMultiple Correct
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

20Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isMultiple Correct
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

JEE Advanced Integer Type

1A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?Integer Type
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

2A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesInteger Type
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

3Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isInteger Type
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

4Multiple correct: In pure magnetic fieldInteger Type
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

5Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isInteger Type
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

6A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?Integer Type
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

7A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesInteger Type
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

8Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isInteger Type
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

9Multiple correct: In pure magnetic fieldInteger Type
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

10Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isInteger Type
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

11A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?Integer Type
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

12A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesInteger Type
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

13Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isInteger Type
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

14Multiple correct: In pure magnetic fieldInteger Type
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

15Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isInteger Type
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

Matrix Match and Paragraph Type

1A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?Advanced Pattern
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

2A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesAdvanced Pattern
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

3Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isAdvanced Pattern
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

4Multiple correct: In pure magnetic fieldAdvanced Pattern
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

5Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isAdvanced Pattern
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

6A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?Advanced Pattern
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

7A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesAdvanced Pattern
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

8Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isAdvanced Pattern
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

9Multiple correct: In pure magnetic fieldAdvanced Pattern
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

10Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isAdvanced Pattern
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

11A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?Advanced Pattern
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

12A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesAdvanced Pattern
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

13Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isAdvanced Pattern
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

14Multiple correct: In pure magnetic fieldAdvanced Pattern
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

15Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isAdvanced Pattern
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

16A charge enters a region with E upward and B into page. It moves right undeflected. Which force is downward?Advanced Pattern
A) Electric
B) Magnetic
C) Both
D) None
Correct Answer and Explanation

Answer: B. For positive charge moving right with B into page, magnetic force is upward/downward based orientation; balance requires opposite electric force. Draw cross product carefully.

17A particle accelerated by V moves in radius r in B. If V is quadrupled, radius becomesAdvanced Pattern
A) r/2
B) r
C) 2r
D) 4r
Correct Answer and Explanation

Answer: C. r is proportional to sqrt(V).

18Two ions have same charge and same accelerating voltage. Radius ratio r1/r2 in same B isAdvanced Pattern
A) sqrt(m1/m2)
B) m1/m2
C) q1/q2
D) 1
Correct Answer and Explanation

Answer: A. r=sqrt(2mV/q)/B.

19Multiple correct: In pure magnetic fieldAdvanced Pattern
A) speed constant
B) kinetic energy constant
C) momentum vector constant
D) force perpendicular to velocity
Correct Answer and Explanation

Answer: A,B,D. Momentum direction changes but magnitude remains constant.

20Integer type: If q/m=4 x 10^7 and B=0.5 T, omega in 10^7 rad/s isAdvanced Pattern
A) 1
B) 2
C) 3
D) 4
Correct Answer and Explanation

Answer: B. omega=(q/m)B=2 x 10^7 rad/s.

IB, ICSE, IGCSE and British Curriculum Questions

1State magnetic force on a moving charge.International Curriculum
Answer / Solution

A moving charge q with velocity v in magnetic field B experiences force F=q(v x B).

2Why is force zero when charge moves parallel to B?International Curriculum
Answer / Solution

Because theta is 0 or 180 degrees and sin theta is zero.

3What is Lorentz force?International Curriculum
Answer / Solution

The total force on a charge in electric and magnetic fields: F=q(E+v x B).

4What do dots and crosses represent?International Curriculum
Answer / Solution

Dots show B out of plane; crosses show B into plane.

5Why does magnetic force do no work?International Curriculum
Answer / Solution

It is always perpendicular to velocity, so F dot displacement is zero.

6Define one tesla.International Curriculum
Answer / Solution

One tesla is magnetic field that exerts 1 N force on 1 A m conductor perpendicular to field.

7What is velocity selector?International Curriculum
Answer / Solution

Crossed E and B field arrangement that allows only speed v=E/B to pass undeflected.

8What is pitch of helix?International Curriculum
Answer / Solution

Distance travelled parallel to magnetic field in one complete revolution.

9What is specific charge?International Curriculum
Answer / Solution

Charge-to-mass ratio q/m of a particle.

10What is cyclotron frequency?International Curriculum
Answer / Solution

Frequency of circular motion f=qB/(2 pi m).

11A proton of speed 2 x 10^6 m/s enters B=0.5 T perpendicularly. Find radius. Take m/q=1.04 x 10^-8 kg/C.International Curriculum
Answer / Solution

r=mv/qB=(m/q)v/B=1.04e-8 x 2e6/0.5=0.0416 m.

12In a velocity selector E=4 x 10^4 V/m and B=0.2 T. Find selected speed.International Curriculum
Answer / Solution

v=E/B=2 x 10^5 m/s.

13A particle has q/m=5 x 10^7 C/kg and moves in B=0.1 T. Find angular frequency.International Curriculum
Answer / Solution

omega=qB/m=(q/m)B=5 x 10^6 rad/s.

14If speed is doubled in same B, what happens to radius?International Curriculum
Answer / Solution

Radius doubles because r is proportional to v.

15If B is doubled, what happens to time period?International Curriculum
Answer / Solution

T becomes half because T is inversely proportional to B.

16An electron accelerated by V enters B perpendicular. Which formula gives q/m?International Curriculum
Answer / Solution

q/m=2V/(B^2r^2).

17Cyclotron CaseInternational Curriculum
Answer / Solution

A charged particle rotates in a cyclotron under uniform magnetic field. Explain why frequency is nearly constant and why radius increases.

18Mass Spectrometer CaseInternational Curriculum
Answer / Solution

Ions accelerated through same potential enter same magnetic field and form different radii.

19Velocity Selector CaseInternational Curriculum
Answer / Solution

A beam passes through crossed electric and magnetic fields and only one speed goes undeflected.

20Electron Beam CaseInternational Curriculum
Answer / Solution

Electron beam bends in a magnetic field in a cathode ray tube.

21Space Physics CaseInternational Curriculum
Answer / Solution

Charged particles spiral around Earth's magnetic field lines.

22State magnetic force on a moving charge.International Curriculum
Answer / Solution

A moving charge q with velocity v in magnetic field B experiences force F=q(v x B).

23Why is force zero when charge moves parallel to B?International Curriculum
Answer / Solution

Because theta is 0 or 180 degrees and sin theta is zero.

24What is Lorentz force?International Curriculum
Answer / Solution

The total force on a charge in electric and magnetic fields: F=q(E+v x B).

25What do dots and crosses represent?International Curriculum
Answer / Solution

Dots show B out of plane; crosses show B into plane.

26Why does magnetic force do no work?International Curriculum
Answer / Solution

It is always perpendicular to velocity, so F dot displacement is zero.

27Define one tesla.International Curriculum
Answer / Solution

One tesla is magnetic field that exerts 1 N force on 1 A m conductor perpendicular to field.

28What is velocity selector?International Curriculum
Answer / Solution

Crossed E and B field arrangement that allows only speed v=E/B to pass undeflected.

29What is pitch of helix?International Curriculum
Answer / Solution

Distance travelled parallel to magnetic field in one complete revolution.

30What is specific charge?International Curriculum
Answer / Solution

Charge-to-mass ratio q/m of a particle.

31What is cyclotron frequency?International Curriculum
Answer / Solution

Frequency of circular motion f=qB/(2 pi m).

32A proton of speed 2 x 10^6 m/s enters B=0.5 T perpendicularly. Find radius. Take m/q=1.04 x 10^-8 kg/C.International Curriculum
Answer / Solution

r=mv/qB=(m/q)v/B=1.04e-8 x 2e6/0.5=0.0416 m.

33In a velocity selector E=4 x 10^4 V/m and B=0.2 T. Find selected speed.International Curriculum
Answer / Solution

v=E/B=2 x 10^5 m/s.

34A particle has q/m=5 x 10^7 C/kg and moves in B=0.1 T. Find angular frequency.International Curriculum
Answer / Solution

omega=qB/m=(q/m)B=5 x 10^6 rad/s.

35If speed is doubled in same B, what happens to radius?International Curriculum
Answer / Solution

Radius doubles because r is proportional to v.

36If B is doubled, what happens to time period?International Curriculum
Answer / Solution

T becomes half because T is inversely proportional to B.

37An electron accelerated by V enters B perpendicular. Which formula gives q/m?International Curriculum
Answer / Solution

q/m=2V/(B^2r^2).

38Cyclotron CaseInternational Curriculum
Answer / Solution

A charged particle rotates in a cyclotron under uniform magnetic field. Explain why frequency is nearly constant and why radius increases.

39Mass Spectrometer CaseInternational Curriculum
Answer / Solution

Ions accelerated through same potential enter same magnetic field and form different radii.

40Velocity Selector CaseInternational Curriculum
Answer / Solution

A beam passes through crossed electric and magnetic fields and only one speed goes undeflected.

41Electron Beam CaseInternational Curriculum
Answer / Solution

Electron beam bends in a magnetic field in a cathode ray tube.

42Space Physics CaseInternational Curriculum
Answer / Solution

Charged particles spiral around Earth's magnetic field lines.

43State magnetic force on a moving charge.International Curriculum
Answer / Solution

A moving charge q with velocity v in magnetic field B experiences force F=q(v x B).

44Why is force zero when charge moves parallel to B?International Curriculum
Answer / Solution

Because theta is 0 or 180 degrees and sin theta is zero.

45What is Lorentz force?International Curriculum
Answer / Solution

The total force on a charge in electric and magnetic fields: F=q(E+v x B).

46What do dots and crosses represent?International Curriculum
Answer / Solution

Dots show B out of plane; crosses show B into plane.

47Why does magnetic force do no work?International Curriculum
Answer / Solution

It is always perpendicular to velocity, so F dot displacement is zero.

48Define one tesla.International Curriculum
Answer / Solution

One tesla is magnetic field that exerts 1 N force on 1 A m conductor perpendicular to field.

49What is velocity selector?International Curriculum
Answer / Solution

Crossed E and B field arrangement that allows only speed v=E/B to pass undeflected.

50What is pitch of helix?International Curriculum
Answer / Solution

Distance travelled parallel to magnetic field in one complete revolution.

51What is specific charge?International Curriculum
Answer / Solution

Charge-to-mass ratio q/m of a particle.

52What is cyclotron frequency?International Curriculum
Answer / Solution

Frequency of circular motion f=qB/(2 pi m).

53A proton of speed 2 x 10^6 m/s enters B=0.5 T perpendicularly. Find radius. Take m/q=1.04 x 10^-8 kg/C.International Curriculum
Answer / Solution

r=mv/qB=(m/q)v/B=1.04e-8 x 2e6/0.5=0.0416 m.

54In a velocity selector E=4 x 10^4 V/m and B=0.2 T. Find selected speed.International Curriculum
Answer / Solution

v=E/B=2 x 10^5 m/s.

55A particle has q/m=5 x 10^7 C/kg and moves in B=0.1 T. Find angular frequency.International Curriculum
Answer / Solution

omega=qB/m=(q/m)B=5 x 10^6 rad/s.

56If speed is doubled in same B, what happens to radius?International Curriculum
Answer / Solution

Radius doubles because r is proportional to v.

57If B is doubled, what happens to time period?International Curriculum
Answer / Solution

T becomes half because T is inversely proportional to B.

58An electron accelerated by V enters B perpendicular. Which formula gives q/m?International Curriculum
Answer / Solution

q/m=2V/(B^2r^2).

59Cyclotron CaseInternational Curriculum
Answer / Solution

A charged particle rotates in a cyclotron under uniform magnetic field. Explain why frequency is nearly constant and why radius increases.

60Mass Spectrometer CaseInternational Curriculum
Answer / Solution

Ions accelerated through same potential enter same magnetic field and form different radii.

61Velocity Selector CaseInternational Curriculum
Answer / Solution

A beam passes through crossed electric and magnetic fields and only one speed goes undeflected.

62Electron Beam CaseInternational Curriculum
Answer / Solution

Electron beam bends in a magnetic field in a cathode ray tube.

63Space Physics CaseInternational Curriculum
Answer / Solution

Charged particles spiral around Earth's magnetic field lines.

64State magnetic force on a moving charge.International Curriculum
Answer / Solution

A moving charge q with velocity v in magnetic field B experiences force F=q(v x B).

65Why is force zero when charge moves parallel to B?International Curriculum
Answer / Solution

Because theta is 0 or 180 degrees and sin theta is zero.

66What is Lorentz force?International Curriculum
Answer / Solution

The total force on a charge in electric and magnetic fields: F=q(E+v x B).

67What do dots and crosses represent?International Curriculum
Answer / Solution

Dots show B out of plane; crosses show B into plane.

68Why does magnetic force do no work?International Curriculum
Answer / Solution

It is always perpendicular to velocity, so F dot displacement is zero.

69Define one tesla.International Curriculum
Answer / Solution

One tesla is magnetic field that exerts 1 N force on 1 A m conductor perpendicular to field.

70What is velocity selector?International Curriculum
Answer / Solution

Crossed E and B field arrangement that allows only speed v=E/B to pass undeflected.

71What is pitch of helix?International Curriculum
Answer / Solution

Distance travelled parallel to magnetic field in one complete revolution.

72What is specific charge?International Curriculum
Answer / Solution

Charge-to-mass ratio q/m of a particle.

73What is cyclotron frequency?International Curriculum
Answer / Solution

Frequency of circular motion f=qB/(2 pi m).

74A proton of speed 2 x 10^6 m/s enters B=0.5 T perpendicularly. Find radius. Take m/q=1.04 x 10^-8 kg/C.International Curriculum
Answer / Solution

r=mv/qB=(m/q)v/B=1.04e-8 x 2e6/0.5=0.0416 m.

75In a velocity selector E=4 x 10^4 V/m and B=0.2 T. Find selected speed.International Curriculum
Answer / Solution

v=E/B=2 x 10^5 m/s.

76A particle has q/m=5 x 10^7 C/kg and moves in B=0.1 T. Find angular frequency.International Curriculum
Answer / Solution

omega=qB/m=(q/m)B=5 x 10^6 rad/s.

77If speed is doubled in same B, what happens to radius?International Curriculum
Answer / Solution

Radius doubles because r is proportional to v.

78If B is doubled, what happens to time period?International Curriculum
Answer / Solution

T becomes half because T is inversely proportional to B.

79An electron accelerated by V enters B perpendicular. Which formula gives q/m?International Curriculum
Answer / Solution

q/m=2V/(B^2r^2).

80Cyclotron CaseInternational Curriculum
Answer / Solution

A charged particle rotates in a cyclotron under uniform magnetic field. Explain why frequency is nearly constant and why radius increases.

81Mass Spectrometer CaseInternational Curriculum
Answer / Solution

Ions accelerated through same potential enter same magnetic field and form different radii.

82Velocity Selector CaseInternational Curriculum
Answer / Solution

A beam passes through crossed electric and magnetic fields and only one speed goes undeflected.

83Electron Beam CaseInternational Curriculum
Answer / Solution

Electron beam bends in a magnetic field in a cathode ray tube.

84Space Physics CaseInternational Curriculum
Answer / Solution

Charged particles spiral around Earth's magnetic field lines.

85State magnetic force on a moving charge.International Curriculum
Answer / Solution

A moving charge q with velocity v in magnetic field B experiences force F=q(v x B).

86Why is force zero when charge moves parallel to B?International Curriculum
Answer / Solution

Because theta is 0 or 180 degrees and sin theta is zero.

87What is Lorentz force?International Curriculum
Answer / Solution

The total force on a charge in electric and magnetic fields: F=q(E+v x B).

88What do dots and crosses represent?International Curriculum
Answer / Solution

Dots show B out of plane; crosses show B into plane.

89Why does magnetic force do no work?International Curriculum
Answer / Solution

It is always perpendicular to velocity, so F dot displacement is zero.

90Define one tesla.International Curriculum
Answer / Solution

One tesla is magnetic field that exerts 1 N force on 1 A m conductor perpendicular to field.

91What is velocity selector?International Curriculum
Answer / Solution

Crossed E and B field arrangement that allows only speed v=E/B to pass undeflected.

92What is pitch of helix?International Curriculum
Answer / Solution

Distance travelled parallel to magnetic field in one complete revolution.

93What is specific charge?International Curriculum
Answer / Solution

Charge-to-mass ratio q/m of a particle.

94What is cyclotron frequency?International Curriculum
Answer / Solution

Frequency of circular motion f=qB/(2 pi m).

95A proton of speed 2 x 10^6 m/s enters B=0.5 T perpendicularly. Find radius. Take m/q=1.04 x 10^-8 kg/C.International Curriculum
Answer / Solution

r=mv/qB=(m/q)v/B=1.04e-8 x 2e6/0.5=0.0416 m.

96In a velocity selector E=4 x 10^4 V/m and B=0.2 T. Find selected speed.International Curriculum
Answer / Solution

v=E/B=2 x 10^5 m/s.

97A particle has q/m=5 x 10^7 C/kg and moves in B=0.1 T. Find angular frequency.International Curriculum
Answer / Solution

omega=qB/m=(q/m)B=5 x 10^6 rad/s.

98If speed is doubled in same B, what happens to radius?International Curriculum
Answer / Solution

Radius doubles because r is proportional to v.

99If B is doubled, what happens to time period?International Curriculum
Answer / Solution

T becomes half because T is inversely proportional to B.

100An electron accelerated by V enters B perpendicular. Which formula gives q/m?International Curriculum
Answer / Solution

q/m=2V/(B^2r^2).

14. Common Mistakes

Mistake 1

Forgetting sin theta in F=qvB sin theta.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 2

Using total velocity instead of perpendicular component in circular radius.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 3

Not reversing force direction for negative charge.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 4

Confusing dots with crosses.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 5

Applying circular motion when v is parallel to B.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 6

Thinking magnetic force changes speed.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 7

Using qV=mv^2 instead of qV=1/2mv^2.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 8

Writing wrong unit of tesla.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 9

Confusing velocity selector with circular motion.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 10

Mixing Fleming left-hand and right-hand rules.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 11

Forgetting that time period is independent of velocity.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 12

Using degrees without checking sine values.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 13

Ignoring mass-to-charge ratio in radius comparison.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 14

Forgetting pitch in helical motion.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 15

Drawing force parallel to magnetic field.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 16

Using electric field direction for magnetic force direction.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 17

Missing vector nature of v x B.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 18

Writing q/m formula with inverted ratio.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 19

Confusing frequency and angular frequency.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

Mistake 20

Not labelling diagrams in board answers.

Correction: Draw the vector diagram, mark v, B, theta and charge sign before applying formula.

15. Final Revision Section

One-Page Formula Sheet

Vector magnetic force: F = q(v x B)

Magnitude: F = qvB sin theta

Parallel case: theta = 0 or 180, F = 0

Perpendicular case: theta = 90, F = qvB

Lorentz force: F = q(E + v x B)

Radius: r = mv/qB

Accelerated particle speed: v = sqrt(2qV/m)

Radius using V: r = sqrt(2mV/q)/B

Specific charge: q/m = 2V/(B^2 r^2)

Time period: T = 2 pi m/qB

Frequency: f = qB/2 pi m

Angular frequency: omega = qB/m

Helix radius: r = mv sin theta/qB

Pitch: p = v cos theta x 2 pi m/qB

Velocity selector: v = E/B

Tesla: 1 T = 1 N A^-1 m^-1

Dimension of B: [B] = M T^-2 A^-1

Concept Map

Magnetic Field -> Magnetic Force -> Lorentz Force -> Circular Motion -> Helical Motion -> Velocity Selector -> Applications.

NEET and JEE Traps

Charge sign, sin theta, v_perpendicular, dots/crosses, q/m ratio, velocity selector balance and independence of time period are the most common traps.

16. Need Personal Help?

If any concept, derivation, numerical problem, diagram, case study, or advanced question is not clear, students can directly contact Kumar Sir for one-to-one personalized guidance.

Kumar Sir provides personal doubt-solving, conceptual clarity, derivation practice, numerical problem-solving techniques, and advanced Physics mentoring for CBSE, NEET, IIT JEE, JEE Advanced, IB, AP, IGCSE, ICSE and British Curriculum Physics.

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