Question

The total electrostatic potential energy of a two-charge system consisting of point charges \[q_1\] and \[q_2\] separated by distance \[r_{12}\] is:

Options

• \[U = \frac{1}{4\pi\varepsilon_0}\cdot\frac{q_1 q_2}{r_{12}^2}\]

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

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

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

Answer 1

The total work done in assembling the two charges equals the potential energy of the system: \[U = \frac{1}{4\pi\varepsilon_0}\cdot\frac{q_1 q_2}{r_{12}}\]. Its sign follows the product \[q_1 q_2\] — positive for like charges and negative for unlike charges.