Question

find the force on a charge of 1 microcoulomb placed at the centre of a square

Answer 1

let all the charges placed at the corners are positive, so to maintain equilibrium a negative charge must be placed at the center of the square. 

Now what remains is to calculate the magnitude of this negative charge. To calculate, you can use the coulumb's law for force. Since the system is in equilibrium, net force on any charged body in the system will be zero. So to calculate the center charge, take the net force on a corner charge due to all other charges to be zero.