Question

A charge is to be divided in to two small objects. What should be the value of the charge on rhe objects so that force between the objects will be maximum?

Answer 1

Let the total charge be Q.
Let charge on first object be x.
So charge on 2nd object is Q-x.

Force between the objects is proportional to x(Q-x).
Differentiating this we get Q-2x.
Equating this to 0.
Q-2x=0
x=Q/2

So charge on each object should be Q/2.