Q. Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius $R$ with constant speed $v.$ The time period of the motion
A) Depends on $v$ and not on $R$
B) Depends on both $R\ and\ v$
C) Is independent of both $R\ and\ v$
D) Depends on $R$ and not on $v$
Explanation
(c) When magnetic field is perpendicular to motion of charged particle, then
Centripetal force = magnetic force
$ie,\ \ \frac{mv^{2}}{R} = Bqv$
or $R = \frac{mv}{Bq}$
Further, time period of the motion
$T = \frac{2\pi R}{v} = \frac{2\pi\left( \frac{mv}{Bq} \right)}{v}$
or $T = \frac{2\pi m}{Bq}$
It is independent of both $R\ \ and\ v.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.