2.11 Electrical Potential Energy

Electric Potential Energy Basics

Electrical potential energy (U) is the energy stored due to the relative positions of charges. For two point charges, U = kq₁q₂/r. Like charges (same sign) have positive U, which decreases as they separate. Opposite charges have negative U, becoming more negative as they get closer, reflecting attraction versus repulsion.

Work and Energy Changes

The work done by the electric force on a charge equals the negative change in potential energy: W = -ΔU. If an external agent moves a charge, work done against the field increases U. Moving a positive charge from low to high potential requires positive work, increasing its electric potential energy.

Conservation of Energy

In systems with only electric forces, total mechanical energy (kinetic + electric potential) is conserved. As charges move under mutual attraction or repulsion, U converts to kinetic energy (KE) or vice versa. This mirrors gravitational PE concepts but depends on charge sign and magnitude rather than mass.

Key terms

Electric Potential Energy Formula

U = kq₁q₂/r, the energy stored due to the relative position of two point charges.

Sign of U for like charges

Positive — repulsive forces mean energy increases as charges are pushed closer together.

Sign of U for opposite charges

Negative — attractive forces mean energy becomes more negative as charges get closer.

Work-Energy Relationship

W = -ΔU: work done by the electric force equals the negative change in potential energy.

Conservation of Energy (electric systems)

Total mechanical energy (KE + U) remains constant when only electric forces act on the system.

Try an AP-style question

Two positive charges are pushed closer together. What happens to the system's potential energy?

1. It stays the same
2. It becomes zero
3. It increases
4. It decreases