Q. A proton, a deutron and a $\alpha$- particle enter a magnetic field perpendicular to field with same velocity. What is the ratio of the radii of circular paths?
A) 1 : 2 : 2
B) 2 : 1 : 1
C) 1 : 1 : 2
D) 1 : 2 : 1
Explanation
(a) $r = \frac{mv}{Bq}\ \ \ \ or\ \ \ \ r \propto \frac{m}{q}$ for the same value of $v\ \ and\ B.$
$\therefore\ \ \ r_{P}\ :r_{d}\ :r_{\alpha} = \frac{m_{P}}{q_{D}}\ :\frac{m_{d}}{q_{d}}\ :\frac{m_{\alpha}}{q_{\alpha}}\ $
$= \frac{m}{l}\ :\frac{2m}{l}\ :\frac{4m}{2l} = 1\ :2\ :2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.