Question

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

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

Answer 1

Answer: (D)

Magnetic force $F =q\,vB\,...(i)$
Centripetal force
$F=\frac{mv^{2}}{r} \,...\left(ii\right)$
From Eqs. $\left(i\right)$ and $\left(ii\right).$
$\frac{mv^{2}}{r}=qvB$
$r=\frac{mv}{qB}$
The time taken by the particle to complete one revolution,
$T=\frac{2\pi r}{v}$
$=\frac{2\pi\,mv}{vqB}$
$=\frac{2\,\pi m}{qB}$