How does potential energy change with distance for opposite vs like charges?

• A. Potential energy increases as opposite charges get farther apart and decreases as like charges get farther apart.
• B. Potential energy increases with distance for like charges and decreases for opposite charges.
• C. Potential energy remains constant regardless of distance.
• D. Potential energy only depends on velocity.

Answer: (A)

The distance dependence of the potential energy between two charges follows U = k q1 q2 / r. The sign of q1 q2 sets whether the energy is negative or positive. For opposite charges, q1 q2 is negative, so U is negative and increases (toward zero) as the separation r grows; as they get closer, r decreases and U becomes more negative (decreases). For like charges, q1 q2 is positive, so U is positive and decreases as r grows; as they get closer, r decreases and U increases. In both cases, U → 0 as r → ∞. So potential energy increases with distance for opposite charges and decreases with distance for like charges.