Q.Three equal point charges, each of $+2\ \mu\text{C}$, are placed at the three corners of an equilateral triangle of side $0.3\ \text{m}$. Find the total electrostatic potential energy of this system.

The total potential energy is the work done against the external field to place each charge, plus the mutual interaction energy of the two charges.

Let $V(r_1)$ and $V(r_2)$ be the potentials due to the external field $\vec E$ at positions $r_1$ and $r_2$.

Step 1 — bring $q_1$ from infinity to $r_1$: Work done against the external field $= q_1V(r_1)$. (No other charge is present yet, so this is the only contribution.)

Step 2 — bring $q_2$ from infinity to $r_2$: Work is done against two fields — the external field, and the field of $q_1$ (now fixed at $r_1$):

$W_2 = q_2V(r_2) + \frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r_{12}}$ …