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Four electric charges +q, +q, $-$ q and $-$ q are placed at the corners of a square of side 2L. The electric potential at point A, midway between the two charges +q and +q, is:

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$\frac{1}{4 {πε}_{0}} \frac{2 q}{L} (1 + \sqrt{5})$

$\frac{1}{4 {πε}_{0}} \frac{2 q}{L} (1 + \frac{1}{\sqrt{5}})$

$\frac{1}{4 {πε}_{0}} \frac{2 q}{L} (1 - \frac{1}{\sqrt{5}})$

answer is B.

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Detailed Solution

Potential, $V = \frac{1}{4 {πε}_{0}} \frac{q}{r}$

Here, $V = 2 V_{+ ve} + 2 V_{- ve}$

$V = \frac{1}{4 {πε}_{0}} [\frac{2 q}{L} - \frac{2 q}{L \sqrt{5}}]$

The electric potential at mid-point A,

$V = \frac{2 q}{4 {πε}_{0} L} (1 - \frac{1}{\sqrt{5}})$

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