First slide

Motion of charged particle in uniform electric field

Question

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 an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio of $t_{2} / t_{1}$ is nearly equal to

Moderate

A

1
B

${(m_{p} / m_{e})}^{1 / 2}$
C

${(m_{e} / m_{p})}^{1 / 2}$
D

$m_{p} / m_{e}$

Solution

$\begin{array}{l} For electron, s = \frac{1}{2} \frac{eE}{m_{p}} \times t_{1}^{2} \\ For proton, s = \frac{1}{2} \frac{eE}{m_{p}} \times t_{2}^{2} \\ ∴ \frac{t_{2}^{2}}{t_{1}^{2}} = \frac{m_{p}}{m_{e}} \Rightarrow \frac{t_{2}}{t_{1}} = \sqrt{\frac{m_{p}}{m_{e}}} = {(\frac{m_{p}}{m_{e}})}^{1 / 2} \end{array}$

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