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 $Randv$
• C. Is independent of both $Randv$
• D. Depends on $R$ and not on $v$

Answer 1

Answer: (C)

When magnetic field is perpendicular to motion of charged particle, then
Centripetal force = magnetic force
$ie,\frac{m{v}^2}{R}=Bqv$
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 $Randv.$