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, $Bq v = \frac{mv^{2}}{r} $
$\Rightarrow Bq = m \omega$
$ \Rightarrow B q =m2 \pi f $ (as $v = r \omega $)
$ \therefore f = \frac{Bq}{2\pi m}$