Electric Potential Energy

Electric potential energy is the energy required to assemble a system of charged particles from an infinite distance. It depends on the separation between charges and the charge magnitude of each object. This energy is a function of position rather than the path taken, making it useful for analyzing charge systems without calculating work directly.

When opposite charges attract, the Coulomb force accelerates the test charge toward the static charge, decreasing the system's potential energy. This is analogous to an object falling under gravity, where electric potential energy converts into kinetic energy. The attractive force does positive work, causing potential energy to decrease.

Like charges repel each other through the Coulomb force, so moving them closer requires external work against the repulsive force. This work increases the system's potential energy. Conversely, when like charges move apart, the repulsive force does positive work and potential energy decreases.

In conservative force systems like electrostatics, the change in potential energy is compensated by an equal and opposite change in kinetic energy, keeping total energy constant. When potential energy decreases, kinetic energy increases, and vice versa. This energy conservation principle applies regardless of the path taken.

Both Coulomb and gravitational forces are conservative, meaning work is path-independent. However, the Coulomb force can be attractive or repulsive depending on charge signs, while gravity is always attractive. This allows electric potential energy to increase or decrease based on charge type, unlike gravity which only decreases with distance.

Electric potential energy is path-independent because the Coulomb force is conservative. The work done by a conservative force depends only on initial and final positions, not the route taken. This property makes potential energy a more practical tool than calculating work for every possible path in complex charge systems.

The work done by the electric field on a charge equals the negative change in potential energy. When the field does positive work, potential energy decreases; when the field does negative work, potential energy increases. This relationship is expressed mathematically as W = -ΔU, connecting field work to energy transformations in electric potential energy in a uniform electric field.