Question

Three point charges $1C,2Cand-2C$ are placed at the vertices of an equilateral triangle of side 1 metre. The work done in joules by an external force to increase the separation of the charges to $2$ metres is :

• A. $\frac{1}{2\pi {ϵ}_0}$
• B. $\frac{1}{8\pi {ϵ}_0}$
• C. $\frac{1}{16\pi {ϵ}_0}$
• D. $0$

Answer 1

The correct option is A $\frac{1}{2\pi {ϵ}_0}$

Potential energy $U=\frac{k{q}_1{q}_2}{r}$
total P.E of system $=P.E{.}_{AB}+P.E{.}_{AC}+P.E{.}_{AC}$

$=\frac{k\left(1\right)\left(2\right)}{r}+\frac{k\left(1\right)(-2)}{r}+\frac{k\left(2\right)(-2)}{r}$

$=\frac{k}{r}(2-2-4)$

$U=-\frac{4k}{r}$
Now work done to separate charges $W=\Delta U$

$=U_2-U_1$

$=(-\frac{4k}{r_2})-(-\frac{4k}{r_1})$

$=-\frac{1}{\pi {ϵ}_{0}2}+\frac{1}{\pi {ϵ}_{0}1}$

$W=\frac{1}{2\pi {ϵ}_0}$