Coulombpotential

Coulombpotential, typically referred to as the Coulomb potential, is the electrostatic scalar potential associated with electric charges. It is the function V(r) whose negative gradient equals the electric field, E = -∇V. For a single point charge q located at the origin, the potential at distance r is V(r) = (1 / (4 π ε0)) (q / r) in SI units. The potential energy of a second charge q' in that field is U(r) = q' V(r) = (1 / (4 π ε0)) (q q' / r). Different unit systems yield V(r) = q/r in Gaussian units.

Mathematically, the Coulomb potential is central and spherically symmetric. In regions containing charge density ρ, it satisfies Poisson's equation ∇^2 V = -ρ / ε0; in charge-free regions, ∇^2 V = 0 (Laplace's equation), with boundary conditions determined by the charge configuration. At large distances from finite charges, V(r) typically falls off as 1/r.

In quantum mechanics and chemistry, the Coulomb potential plays a key role as the electron–nucleus interaction, V(r) = -Z e^2 / (4 π ε0 r) for a nucleus of charge Ze. It underpins the hydrogen atom and many atomic and molecular systems; solutions to the Schrödinger equation in this potential yield bound states with characteristic energy levels.

Limitations include the finite size of charge distributions and screening effects, which modify the short-range behavior. The concept is named after Charles-Augustin de Coulomb.