Question

Two point charges q1 and q2 are located at q and r2, respectively in an external electric field E. Obtain the expression for the total work done in assembling this configuration. ​

Answer 1

Answer: $W = q_{1}Er_{1} + q_{2}Er_{2} + \dfrac{kq_{1}q_{2}}{r_{12}}$

Explanation:

Given that,

First charge = $q_{1}$

Second charge = $q_{2}$

External electric field = E

First charge located at $r_{1}$ and second charge located at $r_{2}$.

The work done for first point charge

$W_{1} = q_{1}Er_{1}$

The work done for second point charge

$W_{2} = q_{2}E r_{2}$

Now, the work done on second charge  to move opposite to first charge

$W_{3} = \dfrac{k q_{1}q_{2}}{r_{12}}$

Now, the total work done is

$W = W_{1} + W_{2} + W_{3}$

$W = q_{1}Er_{1} + q_{2}Er_{2} + \dfrac{kq_{1}q_{2}}{r_{12}}$

Hence, the total work done is $W = q_{1}Er_{1} + q_{2}Er_{2} + \dfrac{kq_{1}q_{2}}{r_{12}}$.