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) → \( -q \)
The potential energy of a system of charges is the sum of the energies of every pair. Let the side of the triangle be \( a \); all three pairs are at the same distance \( a \).
\( \displaystyle U = \frac{1}{4\pi\varepsilon_0\,a}\left[Q(2q) + Q(2q) + (2q)(2q)\right] \)
Setting \( U = 0 \):
\( \displaystyle 4qQ + 4q^{2} = 0 \)
\( \displaystyle Q = -q \)