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)

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