Question

A charged particle is moving in a magnetic field of strength $B$ perpendicular to the direction of the field. If $q$ and $m$ denote the charge and mass of the particle respectively. Then the frequency of rotation of the particle is

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

Answer 1

Answer: (D)

Lorentz force = centripetal force
i.e, $Bqv=\frac{m{v}^2}{r}$
$\Rightarrow Bq=m\omega$
$\Rightarrow Bq=m2\pi f$ (as $v=r\omega$)
$\therefore f=\frac{Bq}{2\pi m}$