Question

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 $

Answer 1

Answer: (C)

To move on circular path in a magnetic field, a centripetal force is provided by the magnetic force.
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 $v$.