Question

A charge having magnitude Q is divided into two parts q and (Q-q) which are held a certian distance r apart. The force of repulsion between the two parts will be maximum if the ratio $\frac{q}{Q}$ is

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

Answer 1

The correct option is A

$\frac{1}{2}$

The force of repulsion between the two parts is given by
$F=\frac{1}{4\pi {ϵ}_0}.\frac{q(Q-q)}{r^2}$
For F to be maximum, $\frac{dF}{dq}=0$, i.e.
$\frac{d}{dq}[\frac{1}{4\pi {ϵ}_0}.\frac{q(Q-q)}{r^2}]=0$
Since r is fixed, we have
$\frac{d}{dq}\left[q\right(Q-q\left)\right]=0or1(Q-q)+q(0-1)$
=0 or $\frac{q}{Q}=\frac{1}{2}$
Hence the correct choice is (a).