Question

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

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

Answer 1

Answer: (B)

$F_{q}=\frac{k q(Q-q)}{L^{2}}=\frac{k}{L^{2}}\left(q Q-q^{2}\right)$
$\frac{d F}{d q}=0$ when force is maximum
$\frac{d F}{d q}=\frac{k}{L^{2}}[Q-2 q]=0 $
$\Rightarrow Q-2 q=0 $
$\Rightarrow Q=2 q$