Question

Three point charges +Q, +Q, and -Q are placed at the corners of an equilateral triangle of side a. What is the total electrostatic potential energy of the system?

• A. \( \frac{kQ^2}{a} \)
• B. 0
• C. \( \frac{a}{3kQ^2} \)
• D. \( \frac{a}{3Q^2} \)

Hint:

In problems involving point charges, always sum up the potential energy contributions for each unique pair of charges.

Answer 1

The Correct Option is C

The total electrostatic potential energy of a system of charges is obtained by summing the potential energies of all charge pairs. The electrostatic potential energy between two charges, \( q_1 \) and \( q_2 \), separated by a distance \( r \), is given by the formula: \[ U = \frac{k q_1 q_2}{r} \] To determine the total potential energy for this system, we compute the potential energy for every pair of charges and then aggregate these values. The final calculated total electrostatic potential energy is \( \frac{a}{3kQ^2} \).