Four equal point charges each of magnitude +Q are to be placed in equilibrium at the corners of a square. A point charge that should be placed at the centre to do this job must have a magnitude $\frac{Q}{4} (x \sqrt{2} + y)$ . Then the value of $x + y$ is _____

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answer is 3.

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Detailed Solution

The net force acting on all the charges must be zero.

$\frac{kqQ}{(l / \sqrt{2})^{2}} = \frac{kQQ}{(\sqrt{2} l)^{2}} + \sqrt{2} \frac{kQQ}{l^{2}}$

$\Rightarrow q = \frac{Q}{4} [2 \sqrt{2} + 1] ∴ x + y = 2 + 1 = 3$

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