Question

Three point charges \( q \), \( 2q \) and \( nq \) are placed at the vertices of an equilateral triangle. If the potential energy of the system is zero, find the value of \( n \).

Answer 1

Finding the value of \( n \): Potential Energy of the System} The potential energy of the system is given by: \[ U = \frac{k q q_2}{a} + \frac{k q_2 q_3}{a} + \frac{k q_3 q}{a} \] Substituting given values: \[ U = \frac{k (q)(2q)}{a} + \frac{k (2q)(nq)}{a} + \frac{k (q)(nq)}{a} = 0 \] \[ \frac{2q^2}{a} + \frac{2nq^2}{a} + \frac{nq^2}{a} = 0 \] \[ 2 + 2n + n = 0 \quad \Rightarrow \quad 3n = -2 \] \[ n = -\frac{2}{3} \]