Three point charges, $q_{1}, q_{2}$, and $q_{3}$, are located at the vertices of an equilateral triangle. If $q_{1}=q_{2}$, what value must $\mathrm{q}_{3}$ have so that the total potential energy of the arrangement is zero?

Question

Quizplus · Accepted Answer

The potential energy between two charges is given by $ k \frac{q_i q_j}{r} $. For the total potential energy to be zero, the sum of the potential energies of all pairs must be zero. Since $ q_1 = q_2 $, the potential energy between $ q_1 $ and $ q_2 $ is positive. To cancel this, $ q_3 $ must be negative and equal in magnitude to half of $ q_1 $ or $ q_2 $, hence $ q_3 = -0.5 q_1 $.

Three Point Charges q1,q2q_{1}, q_{2}q1​,q2​ , And q3q_{3}q3​ , Are Located at the Vertices of an Equilateral Triangle

Three Point Charges $q_{1}, q_{2}$ , And $q_{3}$ , Are Located at the Vertices of an Equilateral Triangle