Question

Three particles, each having a charge of $10\mu C$ are placed at the corners of an equilateral triangle of side $10cm$. The electronic potential energy of the system is: (Given $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^{9}N-m^2/C^2$)

• A. $Zero$
• B. Infinite
• C. $27J$
• D. $100J$

Answer 1

The correct option is C $27J$

Three particles are situated at A,B and C having charge $Q=10\mu C$ each.

The distance between the two charges $r=10cm=0.1$ $m$

Potential energy of the charges at A and B, $E_{AB}=\frac{1}{4\pi {ϵ}_o}\frac{Q^2}{r}$

$\therefore$ $E_{AB}=\frac{9\times {10}^9\times (10\times {10}^{-6}{)}^2}{0.1}=9J$

Similarly, $E_{BC}=E_{AC}=9J$

Total potential energy of the system, $E=E_{AB}+E_{BC}+E_{AC}=27J$