Question

The cyclotron frequency $v_c$ is given by:

• A. $\frac{qB}{2\pi m}$
• B. $\frac{mB}{2\pi q}$
• C. $\frac{2\pi m}{qB}$
• D. $\frac{2\pi B}{qm}$

Answer 1

The correct option is A $\frac{qB}{2\pi m}$

In cyclotron the centripetal force is balanced by magnetic force, then
$qvB=\frac{m{v}^2}{r}\Rightarrow \frac{qBr}{m}=v$
where $v=2\pi r{v}_c$
$\frac{qBr}{m}=2\pi r{v}_c\therefore v_c=\frac{qB}{2\pi m}$