Question

A certain charge $Q$ is divided into two parts, $q$ and $Q-q$. How should the charges be divided so that $q$ and $Q-q$ placed at a certain distance apart, experience maximum electrostatic repulsion?

• A. $Q=2q$
• B. $Q=\frac{q}{2}$
• C. $Q=4q$
• D. $Q=3q$

Answer 1

The correct option is A $Q=2q$


$F=\frac{kq(Q-q)}{L^2}=\frac{k}{L^2}(qQ-q^2)$

$\frac{dF}{dq}=0$, when force is maximum.

$\Rightarrow \frac{dF}{dq}=\frac{k}{L^2}[Q-2q]=0$

$\Rightarrow Q-2q=0\Rightarrow Q=2q$

Hence, option $\left(B\right)$ is the correct answer.