2.5 Electric Potential Energy

Electric Potential Energy Defined

Electric potential energy (U) is the energy stored due to a charge's position in an electric field. For two point charges, U = kq₁q₂/r. It's a scalar, can be positive or negative, and represents work needed to assemble the charge configuration from infinite separation, where U = 0.

Work and Potential Energy

The work done by the electric force on a charge equals the negative change in potential energy: W_field = -ΔU. If an external agent moves a charge against the field, W_ext = ΔU. Systems tend toward lower U; like charges (positive U) push apart releasing energy, unlike charges (negative U) attract.

Multiple Charges & Systems

For a system of point charges, total U is the sum over all unique pairs: U = k∑(qᵢqⱼ/rᵢⱼ). Building a configuration by bringing charges from infinity one at a time requires calculating incremental work against existing charges already placed, since each new charge interacts with all previously positioned ones.

Key terms

Electric potential energy formula (two point charges)

U = kq₁q₂/r, where r is the separation distance between the charges.

Relationship between work and ΔU

W_field = -ΔU (work by electric force); W_ext = ΔU (work by external agent against the field).

Reference point for U = 0

By convention, potential energy is zero when point charges are infinitely far apart.

Sign of U for like vs. unlike charges

Like charges: U is positive (repulsive). Unlike charges: U is negative (attractive).

Total U for multiple point charges

Sum of the potential energies of every unique pair: U = k∑(qᵢqⱼ/rᵢⱼ).

Try an AP-style question

Two 2 μC charges are 0.3 m apart. What is their potential energy? (k = 9 × 10⁹)

1. 0.12 J
2. 0.36 J
3. 1.2 J
4. 0.04 J