An electric field is a region around charged particles where electric forces act on other charges.An electric field is an invisible force around charged objects. Like water around a magnet creating circles, the electric field draws lines along which a charge will move. When you touch synthetic clothing and hear a crackle, you are feeling the electric field.
Michael Faraday in 1831 introduced the concept of lines of force to visualize electric and magnetic interactions. James Clerk Maxwell in 1864 generalized the discoveries into equations, predicting electromagnetic waves. Hendrik Lorentz introduced the concept of the electromagnetic field as a separate entity and the Lorentz force for moving charges. Henri Poincaré studied the symmetries of Maxwell's equations and pointed out relativistic effects. The development of quantum electrodynamics in the works of Dirac and others built a bridge to the microworld.
The electric field E is defined by the force per unit test charge and obeys superposition. Maxwell's equation ∇·E = ρ/ε₀ (Gauss's law) relates the field to charge density. For electrostatics, the field is conservative, and the potential φ satisfies Poisson's equation. In dynamics, the electric field is also generated by a changing magnetic field (Faraday's law). In the relativistic formulation, the electromagnetic tensor F^{μν} combines the fields E and B. The quantum limit is described by Feynman diagrams with the photon as the U(1) gauge boson. Coulomb's law for a point charge gives E = k q / r².
Lightning is a giant discharge that occurs due to the huge difference in electric fields between clouds and the ground.
| φ | variable | Scalar field configuration — scalar field |
| ∇² | operator | Laplacian (sum of second spatial derivatives) — laplacian operator |
| V | variable | potential energy of electron — potential energy joule |
| z | variable | distance from the metal surface — position metre |
| φ | variable | work function of the metal — work function joule |
| F | variable | applied electric field strength — electric field volt per metre |
| e | constant | charge of a single proton — elementary charge = 1.602176634e-19 coulomb |
| ε0 | constant | ability of vacuum to permit electric field lines — vacuum permittivity = 8.8541878128e-12 farad per metre |
| Δn | variable | Change in refractive index — refractive index change |
| E | variable | Applied electric field — electric field volt per metre |
| r | constant | Pockels coefficient (linear electro-optic coefficient) — pockels coefficient = varies by material (e.g., 30.8e-12 for L metre per volt |
| a | variable | axion field — axion field |
| E | variable | electric field — electric field volt per metre |
| B | variable | magnetic field — magnetic field strength tesla |
| g_{aγγ} | constant | Strength of the interaction between axions and two photons. — axion photon coupling constant = model-dependent |
| a_0 | variable | relativistic intensity parameter (normalized vector potential) — relativistic parameter |
| E_0 | variable | peak electric field amplitude of the laser — electric field volt per metre |
| ω | variable | angular frequency of the laser — angular frequency radian per second |
| e | constant | charge of a single proton — elementary charge = 1.602176634e-19 coulomb |
| m_e | constant | mass of an electron at rest — electron mass = 9.1093837015e-31 kilogram |
| c | constant | universal speed limit of light in vacuum — speed of light = 299792458 metre per second |













