Question

A certain charge $Q$ is divided into two parts $q$ and $Q-q$, which are then separated by a certain distance.What must $q$ be in terms of $Q$ to maximize the electrostatic repulsion between the two charges?

• A. $q=-\frac{Q}{2}$
• B. $q=\frac{Q}{2}$
• C. $q=-Q$
• D. $0$

Answer 1

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

Electrostatic repulsion = $F=\frac{1}{4\pi ϵ}\frac{q(Q-q)}{r^2}$

$\frac{dF}{dq}=\frac{1}{4\pi ϵ}\frac{1}{r^2}(Q-2q)=0\Rightarrow q=\frac{Q}{2}$