# Three charges $q_1, q_2$ and $q_3$ are located at the vertices of an equilateral triangle of side a. Find the electric potential energy of the system.

In absence of any charge
$V_A=0,$
$W_1=(V_A - V_{\infty})q_1=0$---------(1)
$W_2=(V_B-V_{\infty}) q_2$
$\quad= \bigg( \large\frac{Kq_1}{a} -0 \bigg) q_2 = \large\frac{Kq_1 q_2}{a}$--------(2)
$W_3=(V_c-V_{\infty})q_3$
$\quad= \bigg( \large\frac{Kq_1}{a} + \large\frac{Kq_2}{a}-0 \bigg)q_3$
$\qquad=\large\frac{Kq_1q_3}{a}+\frac{K q_1q_3}{a}$ ----------(3)
$W=W_1+W_2+W_3$
$W=\large\frac{Kq_1q_2}{a}+\frac{K q_2q_3}{a}+ \frac{K q_1 q_3}{a}$