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?

Answer 1

Let the parts be separated by distance 'd'

So $F=\frac{kq(Q-q)}{d^2}$

$\frac{dF}{dq}=\frac{k}{d^2}\left[\right(Q-q)-q]=\frac{k}{d^2}(Q-2q)=0$

$Q=2q$

$q=\frac{Q}{2}$