First slide

Electrostatic potential

Question

Four equal charges Q are placed at the four corners of a square of side a each. Work done in removing a charge -Q from its centre to infinity is

Moderate

A

zero
B

$\sqrt{2} Q^{2} / (4 {πε}_{0} a)$
C

$\sqrt{2} Q^{2} / ({πε}_{0} a)$
D

$Q^{2} / (2 {πε}_{0} a)$

Solution

The potential at the center of the square of side a due to four equal charges Q at the corners
$= 4 \times \frac{1}{4 {πε}_{0}} \times \frac{Q}{(a / \sqrt{2})} = \frac{\sqrt{2} \cdot Q}{{πε}_{0} a}$
Work done = potential difference x charge
$= \frac{\sqrt{2} Q}{{πε}_{0} a} \times Q = \frac{\sqrt{2} Q^{2}}{{πε}_{0} a}$

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