Question

Three point charges $3nC,6nC$ and $9nC$ are placed at the comers of an equilateral triangle of side $0.1m$. The potential energy of the system is

• A. $8.91\mu J$
• B. $89100\mu J$
• C. $9.91\mu J$
• D. $99100\mu J$

Answer 1

Answer: (A)

Given, $q_1=3nC=3\times 10^{-9}C$
$q_2=6nC=6\times 10^{-9}C$
$q_3=9nC=9\times 10^{-9}C$
$I_{12}=I_{23}=I_{13}=0.1$
Now, potential energy of the system.
$U=\frac{1}{4\pi {\epsilon }_0}\left[\frac{q_1{q}_2}{I_{12}}+\frac{q_2{q}_3}{r_{23}}+\frac{q_1{q}_3}{I_{13}}\right]$
$U=\frac{9\times 10^9}{0.1}[3\times 6+6\times 9+3\times 9]\times 10^{-18}$
$U=8910\times 10^{-9}J=8.91\mu J$