Question

A charge $q$ is lying at mid-point of the line joining the two similar charges $Q$. The system will be in equilibrium, if the value of $q$ is

• A. $\frac{Q}{2}$
• B. $-\frac{Q}{2}$
• C. $\frac{Q}{4}$
• D. $-\frac{Q}{4}$

Answer 1

Answer: (D)

$-\frac{Q}{4}$

Answer 2

When two charges $q_{1}$ and $q_{2}$ are situated in vacuum at a distance $r$ metre, then the electric potential energy of the system is $U=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q_{1} q_{2}}{r}$ joule
In order that system be in equilibrium, the potential energy of the system should be zero.
$\therefore \Sigma U=\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{q Q}{r / 2}+\frac{q Q}{r / 2}+\frac{Q \times Q}{r}\right]$
$0=\frac{2 q Q}{r}+\frac{2 q Q}{r}+\frac{Q^{2}}{r}$
$\Rightarrow 4 q=-Q$
$\Rightarrow q=-\frac{Q}{4}$