Question

Two positive point charges are a fixed distance apart. The sum of their charges is Q_T. What charge must each have in order to (a) maximise the electric force between them and (b) minimise it?

Answer 1

a)

$F=k\frac{q\cdot(Q_T-q)}{r^2}$

In order for the force to be maximal, the condition $\frac{dF}{dq}=0$ must be fulfilled.

$\frac{dF}{dq}=0\to \frac{d}{dq}(qQ_T-q)=0\to q=Q_T/2$

$q_1=q_2=Q_T/2$ . Answer

b)

If $q_1=Q_T$ and $q_2=0$ then the force between them will be zero, which is the minimum possible force. Answer