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, $\frac{m v^{2}}{R}=B q v$ or $R=\frac{m v}{B q}$
Further, time period of the motion
$T=\frac{2 \pi R}{v}=\frac{2 \pi\left(\frac{m v}{B q}\right)}{v}$
or $T=\frac{2 \pi m}{B q}$ It is independent of both $R$ and $v$.