A certain charge Q is divided into two parts q and Q-q which are then seperated by a certain distance.What must q be iin terms of Qto maximise the electrostatics repulsion between the two charges?
Let, q and (Q-q) and 'r' be the separation between the charges.
The force of repulsion between them is,
Differentiation F w.r.t. q and setting it to zero will give us the extremum force.
For this value of q/Q the force is extremum (minimum or maximum). The force will be maximum if the second differentiation of F is less than zero.
Thus, the force of repulsion is maximum when q = Q/2.