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

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 <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-ujv8sxuykpk59zen.jpg" /> (A) -q (B) (q/2) (C) -2q (D) (- q/2)

Tardigrade Admin · Accepted Answer

Electrostatic potential energy of the system of charges is

U = \frac{1}{4 π \in _{0}} [\frac{Qq}{a} + \frac{Qq}{a} + \frac{q ^{2}}{a}]

U = \frac{1}{4 π \in _{0}} [2 Qq + q^{2}]

Given,

U = 0

2 Qq + q^{2} = 0

Q = - \frac{q}{2}

Q. 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

$- q$

$\frac{q}{2}$

$- 2 q$

$\frac{- q}{2}$

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

Q. 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

−q

2q​

−2q

2−q​