Question

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

• A. $\left(Q/q\right)=\left(4/1\right)$
• B. $\left(Q/q\right)=\left(2/1\right)$
• C. $\left(Q/q\right)=\left(3/1\right)$
• D. $\left(Q/q\right)=\left(5/1\right)$

Answer 1

The correct option is B $\left(Q/q\right)=\left(2/1\right)$

We know that the electrostatic force between two charges is $F=\frac{K{q}_1{q}_2}{r^2}$, where symbols have usual meaning
$\Rightarrow F=\frac{Kq(Q-q)}{r^2}$
Now, as the force is maximum
$\Rightarrow \frac{dF}{dq}=0$
$\Rightarrow \frac{dF}{dq}=\frac{K}{r^2}\left[q\right(-1)+(Q-q\left)1\right]=0$
$\Rightarrow -q+Q-q=0$
$\Rightarrow Q=2q$
$\Rightarrow \frac{Q}{q}=\frac{2}{1}$