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When a positive charge is displaced against (opposite to) the direction of an electric field, which statement is true?

1. the potential energy of the system decreases
2. energy must be supplied by an external agent
3. the field performs positive work on the charge
4. the strength of the field decreases

Correct answer: energy must be supplied by an external agent

Solution

The electric force on a positive charge points along E. Displacing the charge opposite to E means the displacement is against the force, so the field does negative work. By work-energy considerations, an external agent must supply energy, increasing the potential energy of the system. The field strength itself is unaffected by moving a test charge.

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