Four charges each equal to -Q are placed at the four corners of a square and a charge q is at its center. If the system is in equilibrium, the value of q is :

Options

A. `-(Q)/(4) (1 + 2 sqrt(2))`
B. `(Q)/(4) (1 + 2 sqrt(2))`
C. `-(Q)/(2) (1 + 2 sqrt(2))`
D. `(Q)/(2) (1 + 2 sqrt(2))`