Question

Three point charges $3\, nC, 6 \,nC$ and $9\,nC$ are placed at the comers of an equilateral triangle of side $0.1\, m$. 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} =3 nC =3 \times 10^{-9} C $
$q_{2}=6 nC =6 \times 10^{-9} C $
$q_{3} =9 nC =9 \times 10^{-9} C $
$I_{12} =I_{23}= I_{13}=0.1$
Now, potential energy of the system.
$U=\frac{1}{4 \pi \varepsilon_{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} $
$U=8910 \times 10^{-9} J =8.91 \mu \,J$