A charge Q is to be divided on two objects. What should be the values of the charges on the objects so that the force between the objects can be maximum?

Explanation

Suppose one object receives a charge q and the
other Q-q. The force between the objects is
` F= (q(Q-q))/(4piepsilon0 d^2 ),`
where d is the separation between them. For F to be
maximmum, the quantity
`y = q (Q-q ) = Qq- q^2`
Should be maximum. This is the case when,
`(dy)/(dq) = 0 or, Q -2q = 0 or, q =Q/2`
Thus, the charge shuld be divided equally on the two objects.