A particle having mass m and charge q moves in a circular path in a magnetic field of strength B. If the radius of the circular path is r, the time required by this particle to complete one revolution is:
Correct answer: A. 2πm/qB
- A. 2πm/qB
- B. 2πm/qBr
- C. qrB/m
- D. 2πmq/rB
- E. 2mq/rB
Explanation
The correct answer is Option A: 2πm/qB. When a charged particle moves in a magnetic field, the magnetic force acts as the centripetal force required for circular motion. The force on the particle is given by qvB, which equals the centripetal force mv²/r. By equating and solving for the velocity v, we find v = qBr/m. Substituting this into the formula for the period, T = 2πr/v, results in T = 2πm/qB.Option B includes an unnecessary factor of r in the denominator, Option C represents angular frequency instead of the period, Option D incorrectly includes an extra factor of q in the numerator, and Option E omits the necessary factor of π.
This question appeared on the NUMS 2019 (cancelled sitting) paper, which you can sit online with every answer explained.
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About Charged Particle in a Magnetic Field
A charged particle moving through a magnetic field experiences the Lorentz force, which is perpendicular to both its velocity and the field. The motion may be circular or helical, with questions involving radius, angular frequency, time period, and work done. A stationary charge feels no magnetic force.
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