Question

A certain charge $Q$ is divided at first into two parts, $q$ and $Q-q$. Later on, the charges are placed at a certain distance. If the force of interaction between the two charges is maximum, then-

• A. $\frac{Q}{q}=\frac{4}{1}$
• B. $\frac{Q}{q}=\frac{2}{1}$
• C. $\frac{Q}{q}=\frac{3}{1}$
• D. $\frac{Q}{q}=\frac{5}{1}$

Answer 1

The correct option is B $\frac{Q}{q}=\frac{2}{1}$

Charge $Q$ is divided in two parts, $q$ and $Q-q$.

Force between them,
$F=\frac{kq(Q-q)}{r^2}$

For maximum force, $\frac{dF}{dq}=0$

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

$\Rightarrow \frac{Q}{q}=\frac{2}{1}$