Question

Two charges q₁ and q₂ are placed in a region with an external electric field E and corresponding potential V(r). What is the total potential energy of the system?

Options

• \[U = q_1V(r_1) + q_2V(r_2) + \frac{q_1q_2}{4\pi\varepsilon_0 r_{12}}\]

• \[U = \frac{q_1q_2}{4\pi\varepsilon_0 r_{12}}\]

• \[U = q_1V(r_1) - q_2V(r_2) + \frac{q_1q_2}{4\pi\varepsilon_0 r_{12}}\]

• \[U = q_1V(r_1) + q_2V(r_2)\]

Answer 1

The total potential energy consists of three components: the interaction of q1 with the external field (q1V(r1)), the interaction of q2 with the external field (q2V(r2)), and the mutual Coulombic interaction between q1 and q2. These three terms sum to give the complete expression for potential energy in the presence of an external field.