A charge Q is to be divided into two small objects. What should be the value of the charges on the objects so that the force between the objects will be maximum.

Explanation

Let q and (Q-q) be the charges on those bodies
Force between the charges
`F=(1)/(4pi in_(0)) ((Q-q)q)/( r^(2)) rArr q=(Q)/(2)`
For F to be maximum `(dF)/(dq)=0`
`rArr (Q)/(r^(2)) -(2q)/(r^(2))=0 rArr q=(Q)/(2)`
Thus we have to divide charges equally on the objects.