Question

Find the charge Q that should be placed at the center of the square of side 4.80E+0 cm, at the corners of which four identical charges +q = 6 C are placed so that the whole system is in equilibrium.

Answer 1

Let the side of the square be of length a.

The magnitude of the electric force on one charge at the corner due to 3 other charges is

DIstance from the center of the square to one of the corners of the square is

The force due to charge Q at the center on the charge at the corner is

For the system to be in equilibrium the forces F and F_{Q should cancel each other}

This gives

This gives the charge Q that should be placed at the center so that the whole system is in equilibrium