When two like charges are brought together, the potential energy of the system formed will

Analyze the question: We are asked what happens to the electric potential energy when two like charges (both positive or both negative) are pushed closer together.

Concept:

• Like charges repel each other.
• To bring them closer, an external agent must push against this repulsive force. That means work is done against the electric field.
• This work is stored in the system as electric potential energy.
• Potential energy of two point charges: U = kq₁q₂ / r. For like charges, q₁q₂ > 0, so U is positive. As r decreases, U increases.

Step-by-step solution:

1. Like charges repel, so the field pushes them apart.
2. Bringing them together means moving them against that repulsion, so work is done against the field.
3. By energy conservation, the work done is stored as potential energy, so the potential energy increases.
4. Check with the formula: if r gets smaller, kq₁q₂/r gets bigger (for like charges, a positive value), so U increases.

Checking the options:

• A. Increase because work is done against the field. This is correct.
• B. Increase because work is done by the field. Wrong, since the field would push the charges apart, not together.
• C. Decrease because work is done by the field. Wrong, since this describes charges moving apart.
• D. Decrease because work is done against the field. Wrong, since work done against a field raises energy.

Exam tip: Think of compressing a spring. Pushing like charges together is like squeezing a spring, because you do work and store energy. If the charges are unlike, the opposite happens, so bringing them together lowers the potential energy because the field does the work.