Question

Charge q is divided into two part and is placed at some fixed distance apart. What should be the value of the two parts such that force between them is maximum?

Answer 1

Let two parts be $Q$ and $(q-Q)$

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

For maximizing the force, differentiating both sides w.r.t $Q$ and equating ot $0$.

$\frac{dF}{dQ}=\frac{k}{r^2}(q-2Q)=0$

$⟹Q=\frac{q}{2}$

Hence, the two parts of charge should have equal charge each equal to $\frac{q}{2}$