Four charges equal to \( -Q \) are placed at the four corners of a square and a charge \( q \) i...

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Four charges equal to \( -Q \) are placed at the four corners of a square and a charge \( q \) is at its centre. If the system is in equilibrium the value of \( q \) is
(a) \( -\frac{Q}{4}(1+2 \sqrt{2}) \)
(b) \( \frac{Q}{4}(1+2 \sqrt{2}) \)
(c) \( -\frac{Q}{2}(1+2 \sqrt{2}) \)
(d) \( \frac{Q}{2}(1+2 \sqrt{2}) \)
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