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)

is independent of both R and v

Answer 2

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
$T=\frac{2 \pi R}{v}=\frac{2 \pi\left(\frac{m v}{B q}\right)}{v}$
$T=\frac{2 \pi m}{B q}$
It is independent of both $R$ and $v$.