Physics · Electrostatic Potential

What is the electrostatic potential energy of a system of three charges \( q_1, q_2, \text{ and } q_3 \) located at positions \( \mathbf{r}_1, \mathbf{r}_2, \text{ and } \mathbf{r}_3 \) respectively?

1. A
   \( \frac{1}{4\pi\varepsilon_0} ( \frac{q_1 q_2 q_3}{r_{12} + r_{23} + r_{31}} ) \) / \( \frac{1}{4\pi\varepsilon_0} ( \frac{q_1 q_2 q_3}{r_{12} + r_{23} + r_{31}} ) \)
2. B
   \( \frac{1}{4\pi\varepsilon_0 r_{123}} (q_1 + q_2 + q_3) \) / \( \frac{1}{4\pi\varepsilon_0 r_{123}} (q_1 + q_2 + q_3) \)
3. C
   \( \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2 q_3}{r_{12} r_{23} r_{31}} \) / \( \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2 q_3}{r_{12} r_{23} r_{31}} \)
4. D
   \( \frac{1}{4\pi\varepsilon_0} ( \frac{q_1 q_2}{r_{12}} + \frac{q_2 q_3}{r_{23}} + \frac{q_3 q_1}{r_{31}} ) \) / \( \frac{1}{4\pi\varepsilon_0} ( \frac{q_1 q_2}{r_{12}} + \frac{q_2 q_3}{r_{23}} + \frac{q_3 q_1}{r_{31}} ) \)