Q. An electron of mass $m_{e}$ initially at rest moves through a certain distance in a uniform electric field in time $t_{1}.$ A proton of mass $m_{p}$ also initially at rest takes time $t_{2}$ to move through and equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio of $t_{2}/t_{1}$ is nearly equal to
A) 1
B) $\left( m_{p}/m_{e} \right)^{1/2}$
C) $\left( m_{e}/m_{p} \right)^{1/2}$
D) 1836
Explanation
(b) For electron $s = \frac{eE}{m_{e}} \times t_{1}^{2},$ For proton $s = \frac{eE}{m_{p}} \times t_{2}^{2}$
$\therefore\frac{t_{2}^{2}}{t_{1}^{2}} = \frac{m_{p}}{m_{e}} \Rightarrow \frac{t_{2}}{t_{1}} = \sqrt{\frac{m_{p}}{m_{e}}} = \left( \frac{m_{p}}{m_{e}} \right)^{1/2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.