How much work has to be done in assembling three charged particles at the vertices of an equilateral

Question

How much work has to be done in assembling three charged particles at the vertices of an equilateral triangle as shown in figure

Professor PC Thomas Classes · Answer

$\begin{aligned} W_{e x t}+W_{e l} & =0 \ W_{e x t} & =-W_{e l}=\Delta U\end{aligned}$ 
$U=k\left(\frac{q_1 q_2}{r_{12}}+\frac{q_1 q_3}{r_{13}}+\frac{q_2 q_3}{r_{23}}ight)$
$\begin{aligned} U & =k\left(\frac{q_1 q_2}{r}+\frac{q_1 q_3}{r}+\frac{q_2 q_3}{r}ight) \ U & =\frac{k}{r}\left(q_1 q_2+q_1 q_3+q_2 q_3ight)\end{aligned}$