Question

A charge $Q$ is divided into $2$ parts and they are placed at a fixed distance. The force between the charges is always maximum when the charges are

• A. $\frac{Q}{3},\frac{2Q}{3}$
• B. $\frac{Q}{2},\frac{Q}{2}$
• C. $\frac{Q}{4},\frac{3Q}{4}$
• D. $\frac{Q}{5},\frac{4Q}{5}$

Answer 1

The correct option is B $\frac{Q}{2},\frac{Q}{2}$

$F=\frac{K{Q}_1{Q}_2}{r^2}$

$⟹F=\frac{K{Q}_1(Q-Q_1)}{r^2}$

Differentiating both sides with respect to $Q_1-$

$\frac{K}{r^2}(q-2Q_1)=\frac{dF}{d{Q}_1}$

For, force to be maximum, $\frac{dF}{d{Q}_1}=0$

$⟹Q-2Q_1=0$

$⟹Q_1=\frac{Q}{2}$

$Q_2=Q-Q_1=\frac{Q}{2}$

Answer-(B)