Question

Three-point charges \( Q \), \( q \), and \( -q \) are kept at the vertices of an equilateral triangle of side \( L \). What is the total electrostatic potential energy of the system?

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

Hint:

When dealing with electrostatic potential energy in systems of point charges, always remember to account for all pairwise interactions.

Answer 1

The Correct Option is C

Given:

• Three charges: \( Q, q, -q \)
• Positioned at the vertices of an equilateral triangle with side length \( L \)

Electrostatic Potential Energy Formula:

\[ U = \frac{k q_1 q_2}{r} \]

Pairwise Interactions:

1. Interaction between \( Q \) and \( q \): \[ U_1 = \frac{k Q q}{L} \]
2. Interaction between \( Q \) and \( -q \): \[ U_2 = \frac{k Q (-q)}{L} = -\frac{k Q q}{L} \]
3. Interaction between \( q \) and \( -q \): \[ U_3 = \frac{k q (-q)}{L} = -\frac{k q^2}{L} \]

Total Potential Energy:

\[ U_{\text{total}} = U_1 + U_2 + U_3 = \frac{k Q q}{L} - \frac{k Q q}{L} - \frac{k q^2}{L} \] \[ U_{\text{total}} = -\frac{k q^2}{L} \]

✅ Final Answer:

\[ \boxed{U = -\frac{k q^2}{L}} \]