Maxwell's Equations

CORE DEFINITION

Maxwell's equations, or Maxwell-Heaviside equations, are a set of partial differential equations that describe the relationships between electric fields, magnetic fields, charge density, and current density. The set consists of four equations: Gauss's law, which describes how electric charges produce electric fields; Gauss's law for magnetism, which states that magnetic monopoles do not exist; Faraday's law of induction, which explains how time-varying magnetic fields produce electric fields; and Maxwell-Ampère's law, which describes how electric currents and time-varying electric fields produce magnetic fields. Maxwell's equations are named after the British physicist James Clerk Maxwell, who conceived their early form in the 1860s. Different forms of Maxwell's equations are used in various fields. For example, in high-energy physics and gravitational physics, a spacetime formulation of Maxwell's equations is often used. This formulation is based on Einstein's concept of spacetime, which combines time and space, rather than Newton's absolute space and time, where three-dimensional space and the fourth dimension of time are treated separately. Einstein's spacetime formulation is clearly consistent with both special and general relativity.