Q. 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) $f = \frac{qB}{2\pi m}$
B) $f = \frac{qB}{2\pi m^{2}}$
C) $f = \frac{2\pi^{2}m}{qB}$
D) $f = \frac{2\pi m}{qB}$
Explanation
(a) Lorentz force = centripetal force
$ie,\ \ Bqv = \frac{mv^{2}}{r}$
$\Rightarrow Bq = m\omega$
$\Rightarrow Bq = m2\pi f\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (as\ v = r\omega)$
$\therefore\ \ f = \frac{Bq}{2\pi m}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.