First slide

Force on a charged particle moving in a magnetic field

Question

An electron of mass m_e initially at rest' moves through a certain distance in a uniform electric field in time t₁. R 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 t₂ / t₁, is nearly equal to

Moderate

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 $s = \frac{eE}{m_{p}} \times {t_{2}}^{2}$
$∴ \frac{{t_{2}}^{2}}{{t_{1}}^{2}} = \frac{m_{p}}{m_{e}} or \frac{t_{2}}{t_{1}} = \sqrt{(\frac{m_{p}}{m_{e}})}$

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