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.

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