A certain charge Q is to be divided into two parts and q. We have to find the relation of Q to q if the two parts, placed a given distance apart, are to have a maximum Coulomb repulsion.

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It is given that a certain charge Q is to be divided into two parts and q. We have to find the relation of Q to q such that there is maximum Coulomb repulsion for a fixed separation between the two charges.

As the Coulomb force is proportional to the product of the charges, we have to maximise the function

Condition for extremum of this function is

We thus have the equation