Electromagnetic wave
A self-sustaining coupled oscillation of electric and magnetic fields that propagates through vacuum at c = 1/√(μ₀ε₀). E, B, and k are mutually perpendicular. Maxwell's synthesis identified light itself as an electromagnetic wave.
Definition
An electromagnetic wave is a self-sustaining coupled oscillation of electric and magnetic fields propagating through space. The derivation from Maxwell's equations in source-free vacuum is direct: take the curl of Faraday's law (∇×E = −∂B/∂t), substitute Ampère–Maxwell (∇×B = μ₀ε₀ ∂E/∂t), and use the vector identity ∇×(∇×E) = −∇²E (given ∇·E = 0). The result is the wave equation ∇²E = (1/c²) ∂²E/∂t² with c = 1/√(μ₀ε₀). Identical equations govern B. Plane-wave solutions have the form E = E₀ cos(k·r − ωt) with ω = c|k|, and the electric field, magnetic field, and propagation direction form a mutually perpendicular right-handed triad with |B| = |E|/c.
The wave carries energy density u = ½ε₀|E|² + |B|²/(2μ₀), evenly split between the electric and magnetic parts, and transports that energy at speed c in the propagation direction. The instantaneous energy flux is the Poynting vector S = (1/μ₀) E×B, whose time-average gives the intensity. An electromagnetic wave absorbed by a perfectly absorbing surface exerts radiation pressure P = I/c; reflected off a perfect mirror, it delivers 2I/c. Polarisation states (linear, circular, elliptical) encode the two independent transverse degrees of freedom of E. The spectrum spans radio (below 300 GHz), microwaves, infrared, visible light (400–700 nm), ultraviolet, X-rays, and gamma rays — all the same phenomenon, differing only in ω. Maxwell derived these results in 1865; Hertz confirmed them experimentally at radio frequencies in 1887, sealing the synthesis that light is an electromagnetic wave.