An amount of charge Q is distributed between two particles. What should be the charges of the two particles so that the force of interaction between them is maximum?

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Solution

Let the charge Q is divided into two parts of q and Q-q

let parts are sepereted at a distance of d
so repulsion force
F= k q(Q-q)/d^2
here Q and d are constant so for maximum force differentiate the force w.r.t q
dF/dq = k/d^2 [Q -2q]
for maximum force dF/dq=0
Q-2q=0
Q/q =2

So the charges are Q/2 and Q/2

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