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

The correct option is C is independent of both $R$ and $v$

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