First slide

Electric field

Question

An electron of mass m_e initially at rest moves through a certain distance in a uniform electric field in time t₁. A proton of mass m_p also initially at rest takes time t₂ 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

Easy

A

1
B

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

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

1836

Solution

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

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