Three charges Q, $+2q$ and $+2q$ are placed at the vertices of an equilateral triangle. If the net electrostatic potential energy of the system is zero, then Q is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $-q$
$\text{Let side of equilateral triangle} = a$
$U = k\left[\frac{Q \cdot 2q}{a} + \frac{Q \cdot 2q}{a} + \frac{2q \cdot 2q}{a}\right]$
$U = \frac{k}{a}\left[2Qq + 2Qq + 4q^2\right]$
$U = \frac{k}{a}\left[4Qq + 4q^2\right]$
$\text{Given } U = 0$
$4Qq + 4q^2 = 0$
$Qq + q^2 = 0$
$Q + q = 0$
$Q = -q$
Final Answer: $-q$