Question

Three point charges $Q_1=25\mu$C, $Q_2=50\mu$C and $Q_3=100\mu$C, are kept at the corners A, B and C respectively of an equilateral triangle ABC having each side equal to $7.5$m. Calculate the total electrostatic potential energy of the system.

Answer 1

We know, $u=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r}$
So, $u=\frac{1}{4\pi {\epsilon }_0}\left(\frac{q_1{q}_2}{r_1}+\frac{q_2{q}_3}{r_2}+\frac{q_3{q}_1}{r_3}\right)$
where, $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^{9}N{m}^2{C}^{-2}$
$=\frac{9\times {10}^9}{7.5}(25\times {10}^{-6}\times 50\times {10}^{-6}+50\times {10}^{-6}\times 100\times {10}^{-6}+100\times {10}^{-6}\times 25\times {10}^{-6})$
$=10.5$J.