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

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.

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.