Q. Two particles of equal charges after being accelerated through the same potential difference enter a uniform transverse magnetic field and describe circular path of radii $R_{1}\ and\ \ R_{2}$ respectively. Then the ratio of their masses $(M_{1}/M_{2})$ is
A) $\frac{R_{1}}{R_{2}}$
B) $\left( \frac{R_{1}}{R_{2}} \right)^{2}$
C) $\frac{R_{2}}{R_{1}}$
D) $\left( \frac{R_{2}}{R_{1}} \right)^{2}$
Explanation
(b) Radius of circular path
$R = \frac{mv}{qB}$
But $mv = \ \sqrt{2mqV}$
$\therefore R = \frac{\sqrt{2mqV}}{qB}\ \ or\ R \propto \sqrt{m}$
or $\frac{R_{1}^{2}}{R_{2}^{2}} = \frac{M_{1}}{M_{2}}$
or $\frac{M_{1}}{M_{2}} = \frac{R_{1}^{2}}{R_{2}^{2}} = \left( \frac{R_{1}}{R_{2}} \right)^{2}\ $
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.