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

$negative straight Q over 4 space left parenthesis 1 space space plus 2 square root of 2 right parenthesis$
$straight Q over 4 space left parenthesis 1 space space plus 2 square root of 2 right parenthesis$
$negative straight Q over 2 space left parenthesis 1 space plus 2 square root of 2 right parenthesis$
$straight Q over 2 space left parenthesis 1 space plus 2 square root of 2 right parenthesis$

Solution

straight Q over 4 space left parenthesis 1 space space plus 2 square root of 2 right parenthesis

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