# 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

$(a)\;\large\frac{Q}{4} , \large\frac{3Q}{4}\qquad(b)\;\large\frac{Q}{2} , \large\frac{Q}{2}\qquad(c)\;\large\frac{Q}{3} , \large\frac{2Q}{3}\qquad(d)\;None$

Answer : (b) $\;\large\frac{Q}{2} , \large\frac{Q}{2}$
Explanation : Suppose one object receives a charge q and the other Q-q . The force between the objects is
$F=\large\frac{k\;q\;(Q-q)}{d^2}$
For F to be max $\;\large\frac{d F}{dq}=0$
$Q-2q=0$
$q=\large\frac{Q}{2}\;.$