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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 ) $-\frac{Q}{2} (1 + 2 \sqrt{2})$
( C ) $\frac{Q}{2} (1 + 2 \sqrt{2})$
( D ) $\frac{Q}{4} (1 + 2 \sqrt{2})$

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