Question

Three charges are placed at the vertex of an equilateral triangle as shown in figure. The value of $Q$ , for which the electrostatic potential energy of the system is zero, is

• A. $-q$
• B. $\frac{q}{2}$
• C. $-2q$
• D. $\frac{- q}{2}$

Answer 1

Answer: (D)

Electrostatic potential energy of the system of charges is
$U=\frac{1}{4 \pi \in _{0}} \, \left[\frac{Qq}{a} + \frac{Qq}{a} + \frac{q^{2}}{a}\right]$
$U=\frac{1}{4 \pi \in _{0}}\left[2 Qq + q^{2}\right]$
Given, $U=0$
$ \, 2Qq+q^{2}=0 \, $
$Q=-\frac{q}{2}$