Question

The period of revolution of a charged particle inside a cyclotron does not depend on :

• A. The magnetic induction
• B. The charge of the particle
• C. The velocity of the particle
• D. The mass of the particle

Answer 1

Answer: (C)

The velocity of the particle

When the velocity of a charged particle is perpendicular to the uniform magnetic field B, the particle moves in a plane perpendicular to B. This motion is known as cyclotron. Here magnetic force required to keep the particle moving in a circle.

So, $F_B=qvB=\frac{m{v}^2}{r}$

or $r=mv/qB$

The period of revolution, $T=\frac{2\pi r}{v}=\frac{2\pi m}{qB}$

Thus, the period of revolution does not depend on velocity, $v$.