Question

The total electrostatic potential energy of a three-charge system is:

Options

• \[U = \frac{1}{4\pi\varepsilon_0}\left(\frac{q_1 q_2}{r_{12}}\right)\]

• \[U = \frac{1}{4\pi\varepsilon_0}\left(\frac{q_1 + q_2 + q_3}{r}\right)\]

• \[U = \frac{1}{4\pi\varepsilon_0}\left(\frac{q_1 q_2}{r_{12}} + \frac{q_1 q_3}{r_{13}} + \frac{q_2 q_3}{r_{23}}\right)\]

• \[U = \frac{1}{4\pi\varepsilon_0}\cdot\frac{q_1 q_2 q_3}{r_{12} r_{13} r_{23}}\]

Answer 1

The total potential energy of a three-charge system is the sum over all three unique pairs: \[U = \frac{1}{4\pi\varepsilon_0}\left(\frac{q_1 q_2}{r_{12}} + \frac{q_1 q_3}{r_{13}} + \frac{q_2 q_3}{r_{23}}\right)\], which equals \[W_2 + W_3\] since \[W_1 = 0\].