Question

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

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

Answer 1

For a charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to the magnetic field B, we can write,

$\frac{m{v}^2}{r}=Bqv$

$\frac{mv}{r}=Bq$

$v=\frac{Bqr}{m}$

Since, the particle completes one revolution

Hence, $v=\frac{2\pi r}{t}$

$\frac{2\pi r}{t}=\frac{Bqr}{m}$

$t=\frac{2\pi m}{qB}$