As two like charges are brought closer together, what happens to their potential energy?

• A. It increases; U ∝ 1/r
• B. It decreases; U ∝ −1/r
• C. It remains unchanged
• D. It becomes zero at contact

Answer: (A)

When two like charges are brought closer, the system’s electrostatic potential energy changes with the separation r according to U = k q1 q2 / r. Since q1 q2 is positive for like charges, U is positive and scales as 1/r. As r decreases, 1/r increases, so the potential energy increases. This increase reflects the work required to push the charges together against their repulsive electric force. It isn’t zero at contact; the energy would grow without bound as r approaches zero. For contrast, if the charges were opposite, the potential energy would be negative and would decrease in magnitude (become more negative) as they come closer.