Q.
Three charges are placed at the vertex of an equilateral triangle as shown in figure. For what value of$\mathcal{\ Q}$, the electrostatic potential energy of the system is zero?
A) $- q$
B) $\frac{q}{2}$
C) $- 2q$
D) $\frac{- q}{2}$
Explanation
(d) Electrostatic potential energy of the system of charges is
$U = \frac{1}{4\pi\varepsilon_{0}}\left\lbrack \frac{\mathcal{Q}q}{a} + \frac{\mathcal{Q}q}{a} + \frac{q^{2}}{a} \right\rbrack$
$U = \frac{1}{4\pi\varepsilon_{0}a}\left\lbrack 2\mathcal{Q}q + q^{2} \right\rbrack$
Given, $U = 0$
$\Longrightarrow \ \ \ \ \ \ 2\mathcal{Q}q + q^{2} = 0\ $
$\Longrightarrow \ \ \ \mathcal{Q = -}\frac{q}{2}$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.