Question

A charged particle of mass $m$ and charge $q$ travels in a circular trajectory of radius $r$ in a magnetic field $B.$ The time taken by the particle to complete one revolution is

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

Answer 1

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

For the given condition we can write,
$\frac{m{v}^2}{r}=Bqv\Rightarrow v=\frac{Brq}{m}$
Since, the particle completes one revolution
$\Rightarrow v=\frac{2\pi r}{t}=\frac{Brq}{m}$
Therefore, time taken by a particle to complete circular path is
$t=\frac{2\pi m}{qB}$