Question

If three equal charges $q$ are placed at the vertices of an equilateral triangle of side $l$, what is the net potential energy of the system?

• A. $\frac{3q^2}{4\pi {ϵ}_{0}l}$
• B. $\frac{q^2}{2\pi {ϵ}_{0}l}$
• C. $\frac{q^2}{4\pi {ϵ}_{0}l}$
• D. $\frac{q^2}{\pi {ϵ}_{0}l}$

Answer 1

The correct option is A $\frac{3q^2}{4\pi {ϵ}_{0}l}$

$U=\frac{q_1{q}_2}{4\pi {ϵ}_{o}r}$

$U=U_{AB}+U_{BC}+U_{AC}$

$U=\frac{1}{4\pi {ϵ}_o}(\frac{q^2}{l}+\frac{q^2}{l}+\frac{q^2}{l})$

$⟹U=\frac{3q^2}{4\pi {ϵ}_{o}l}$

Answer-(A)