Electricfield

An electric field is a vector field that assigns to every point in space a quantity E describing the force that a positive test charge would experience per unit charge. The force on a test charge q is F = qE, so E = F/q in the limit of a vanishing test charge. The SI units are newtons per coulomb (N/C) or volts per meter (V/m).

For a point charge q at distance r, E(r) = k q / r^2 r̂, where k = 1/(4πε0) and r̂ points away from q for q > 0. For a continuous charge distribution with density ρ(r'), the field is E(r) = ∫ k ρ(r') (r − r')/|r − r'|^3 dV'.

Key laws include Gauss's law ∮ E·dA = Qenc/ε0; in electrostatics curl E = 0, so E = −∇V for an electric potential V. In conductors at electrostatic equilibrium, E = 0 inside; charges reside on surfaces to cancel internal fields.

Time-varying fields obey Maxwell's equations; changing magnetic fields induce electric fields (Faraday's law, ∇×E = −∂B/∂t). Electric fields are central to the description of electromagnetic phenomena and underpin technologies such as capacitors, insulation, sensors, and the propagation of electromagnetic waves.