# Four charges of magnitude - '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 :

$\begin {array} {1 1} (1)\;\large\frac{Q}{4}(1+2\sqrt 2) & \quad (2)\;\large\frac{Q}{4}(1+2\sqrt 2) \\ (3)\;\large\frac{Q}{2}(1+2\sqrt 2) & \quad (4)\;\large\frac{Q}{2}(1+\sqrt 2) \end {array}$

Ans : (2)
$\large\frac{Q}{4}(1+2\sqrt 2)$