Question

The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its :

• A. speed
• B. mass
• C. charge
• D. magnetic induction

Answer 1

Answer: (A)

In a circular motion in a uniform magnetic field, the necessary centripetal force to the charged particle is provided by the magnetic force, i.e.,
$\frac{m{v}^2}{r}=qvB$
or $r=\frac{mv}{qB}$
Thus, the time period $T$ is
$T=\frac{2\pi r}{\nu }=\frac{2\pi }{v}\left(\frac{mv}{qB}\right)=\frac{2\pi m}{qB}$
So, T is independent of its speed.