Question: Q. 11. Two point charges $q_{1}$ and $q_{2}$ are located at $\vec{r}{1}$ and $\overrightarrow{r{2}}$ respectively in an external electric field $E$. Obtain the expression for the total work done in assembling this configuration.
A [Comptt. Delhi I, II, III 2014]
Show Answer
Solution:
Ans. Work done in bringing the charge $q_{1}$ from infinity to the position $\overrightarrow{r_{1}}$
$$ W_{1}=q_{1} V\left(\overrightarrow{r_{1}}\right) $$
Work done in bringing the charge $q_{2}$ to the position $\overrightarrow{r_{2}}$
$W_{2}=q_{2} V\left(\overrightarrow{r_{2}}\right)+\frac{q_{1} q_{2}}{4 \pi \varepsilon_{0} r_{12}}$
$1 / 2+1 / 2$ Hence, total work done in assembling the two charges
$$ \begin{array}{r} W=W_{1}+W_{2} \ W=q_{1} V\left(\overrightarrow{r_{1}}\right)+q_{2} V\left(\overrightarrow{r_{2}}\right)+\frac{q_{1} q_{2}}{4 \pi \varepsilon_{0} r_{12}} \end{array} $$
[CBSE Marking Scheme 2014]
