Q. An electron having kinetic energy $E$ is moving in a circular orbit of radius $R$ perpendicular to a uniform magnetic field induction $\overrightarrow{B}$. If kinetic energy is doubled and magnetic field induction is tripled, the radius will become
A) $R\ \sqrt{9/4}$
B) $R\ \sqrt{3/2}$
C) $R\ \sqrt{2/9}$
D) $R\ \sqrt{4/3}$
Explanation
(c) $\ E = \ \frac{B^{2}q^{2}r^{2}}{2m}\ \ \ \ or\ \ \ r = \frac{\sqrt{2mE}}{Bq}$
So, $r\ \propto \ \sqrt{E}/B$
$\therefore\ \ \ \frac{r_{2}}{r_{1}} = \sqrt{\frac{2E}{E}}\ \times \frac{B}{3B} = \sqrt{\frac{2}{9}}\ $
$\therefore\ \ \ r_{2}\ = \ \sqrt{\frac{2}{9}\ }r_{1} = \sqrt{\frac{2}{9}\ }R.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.