Question

Three point charges, q1, q2, and q3, are located at the vertices of an equilateral triangle. If q1 = q2, what value must q3 have so that the total potential energy of the arrangement is zero?

Answer 1

Potential energy of the system:

$U = \frac{kq_1q_2}{a} + \frac{kq_2q_3}{a} + \frac{kq_3q_1}{a}$

$q_1 = q_2$

U = 0

$0 = \frac{k}{a}[q_1^2 + 2(q_1q_3)]$

$0 = q_1(q_1 + 2q_3)$

$0 = q_1 + 2q_3$

$q_3 = -\frac{q_1}{2}$