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., $\frac{m{v}^2}{r}=qvB$ $r=\frac{mv}{qB}$ Thus, the time period T is $T=\frac{2\pi r}{v}$ $=\frac{2\pi m}{qB}$ So, Tis independent of its speed.