Q. A proton (mass $m$ and charge $+ e$) and an $\alpha$-particle (mass $4m$ and charge $+ 2e$) are projected with the same kinetic energy at right angles to the uniform magnetic field. Which one of the following statements will be true
A) The $\alpha$-particle will be bent in a circular path with a small radius that for the proton
B) The radius of the path of the $\alpha$-particle will be greater than that of the proton
C) The $\alpha$-particle and the proton will be bent in a circular path with the same radius
D) The $\alpha$-particle and the proton will go through the field in a straight line
Explanation
(c) $r = \frac{\sqrt{2mK}}{qB}i.e.r \propto \frac{\sqrt{m}}{q}$
Here kinetic energy $K$ and $B$ are same
$\therefore\frac{r_{p}}{r_{\alpha}} = \frac{\sqrt{m_{p}}}{\sqrt{m_{\alpha}}}.\frac{q_{\alpha}}{q_{p}} = \frac{\sqrt{m_{p}}}{\sqrt{4m_{p}}}.\frac{2q_{p}}{q_{p}} = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.