Question:
A certain charge $\mathrm{Q}$ is divided into two parts $\mathrm{q}$ and (Q-q). How should the charges Q and $q$ be divided so that $\mathrm{q}$ and $(\mathrm{Q}-\mathrm{q})$ placed at a certain distance apart experience maximum electrostatic repulsion?
Correct Option: , 2
Solution:
$\mathrm{F}_{\mathrm{q}}=\frac{\mathrm{kq}(\mathrm{Q}-\mathrm{q})}{\mathrm{L}^{2}}=\frac{\mathrm{k}}{\mathrm{L}^{2}}\left(\mathrm{qQ}-\mathrm{q}^{2}\right)$
$\frac{\mathrm{dF}}{\mathrm{dq}}=0$ when force is maximum
$\frac{\mathrm{dF}}{\mathrm{dq}}=\frac{\mathrm{k}}{\mathrm{L}^{2}}[\overline{\mathrm{Q}}-2 \mathrm{q}]=0$
$\Rightarrow \mathrm{Q}-2 \mathrm{q}=0 \Rightarrow \mathrm{Q}=2 \mathrm{q}$