First slide

Electrostatic potential

Question

An electron having charge e and mass m starts from the lower plate of two metallic plates separated by a distance d. If the potential difference between the plates is V, the time taken by the electron to reach the upper plate is given by

Moderate

A

$\sqrt{\frac{2 {md}^{2}}{eV}}$
B

$\sqrt{\frac{{md}^{2}}{eV}}$
C

$\sqrt{\frac{{md}^{2}}{2 eV}}$
D

$\frac{2 {md}^{2}}{eV}$

Solution

$E = \frac{V}{d}, F = eE = eV / d$
$a = \frac{F}{m} = \frac{eV}{md}$
$d = \frac{1}{2} {at}^{2} or t = \sqrt{\frac{2 d}{a}}$
or $t = \sqrt{\frac{2 dmd}{eV}} = \sqrt{\frac{2 {md}^{2}}{eV}}$

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