Question

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

• A. Zero
• B. $\infty$
• C. 27 J
• D. 100 J

Answer 1

The correct option is C 27 J

Work done in placing first charge at one of the corners=$0$(no other charge present)

Work done in placing second charge at the other corner=$\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_2}{r_{12}}$

Work done in placing third charge=$\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_3}{r_{13}}+\frac{1}{4\pi {ϵ}_0}\frac{q_2{q}_3}{r_{23}}$
Thus the total work done=$\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_2}{r_{12}}+\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_3}{r_{13}}+\frac{1}{4\pi {ϵ}_0}\frac{q_2{q}_3}{r_{23}}=27J$

Hence correct answer is option C.