An Etymological Dictionary of Astronomy and Astrophysics

A set of four fundamental equations that describe the electric and magnetic fields arising from varying electric charges and magnetic fields, electric currents, charge distributions, and how those fields change in time. In their vector differential form, these equations are:

i) ∇.E = ρ/ε₀ (→ Gauss’s law for electricity),

ii) ∇.B = 0 (→ Gauss’s law for magnetism),

iii) ∇ x E = -∂B/∂t (→ Faraday’s law of induction),

iv) ∇ x B = μ₀J + μ₀ε₀∂E/∂t (→ Ampere’s law), with c² = 1/(μ₀ε₀), where

E is → electric intensity, B is → magnetic flux density, ρ is → charge density, ε₀ is → permittivity, μ₀ is → permeability, J is → current density, and c is → speed of light.

See also: → maxwell. It should be emphasized that the equations originally published by James Clerk Maxwell in 1873 (in A Treatise on Electricity and Magnetism)
were 20 in number, had 20 variables, and were in scalar form. The
German physicist Heinrich Rudolf Hertz (1857-1894) reduced them to 12 scalar equations (1884). It was the English mathematician/physicist Oliver Heaviside (1850-1925) who expressed Maxwell’s equations in vector form using the notations of → gradient, → divergence, and → curl of a vector, thus simplifying them to the present 4 equations (1886). Before Einstein these equations were known as Maxwell-Heaviside-Hertz equations, Einstein (1940) popularized the name “Maxwell’s Equations;” → equation.