# Chapter 25 - The Electric Potential - Exercises and Problems - Page 709: 6

$U=0$

#### Work Step by Step

Electric potential Energy of 3 point charge $q_{1},q_{2},$ and $q_{3}$ is given as: $U=\frac{1}{4\pi \epsilon_{0}}$[$\frac{q_{1}q_{2}}{r_{12}}+\frac{q_{2}q_{3}}{r_{23}}+\frac{q_{3}q_{1}}{r_{31}}]$ $=9\times 10^{9} [\frac{(1)(-2)}{3}+\frac{(-2)(-2)}{3}+\frac{(-2)(1)}{3}]\frac{10^{-18}}{10^{-2}}$ $=\frac{9\times 10^{-9}}{10^{-2}\times3}[-2+4-2]$ Hence, $U=0$.

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