Question

The cyclotron frequency $\upsilon_{c}$ 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

Answer: (A)

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