AmpereMaxwell

AmpereMaxwell is a term that refers to the unified form of Ampere's law and Maxwell's correction to electromagnetism, commonly called the Ampere-Maxwell law. It describes how magnetic fields arise from electric currents and from changing electric fields.

In differential form, it is written as curl B = μ0 J + μ0 ε0 ∂E/∂t. In integral form, ∮ B · dl = μ0 I_enclosed + μ0 ε0 dΦ_E/dt.

Historically, Ampere's law described magnetism from steady currents. James Clerk Maxwell added the displacement current term to account for changing electric fields, completing the theory in the 1860s. The equation is sometimes called the Maxwell-Ampere equation, and AmpereMaxwell is used to emphasize this unification.

Significance includes the prediction that varying electric and magnetic fields propagate as electromagnetic waves, with the speed c determined by c = 1/√(μ0 ε0). The law also embodies the continuity equation ∇·J + ∂ρ/∂t = 0.

Applications span radio and wireless communication, antennas, optical and microwave devices, and the broader study of electromagnetic phenomena. Related topics include Maxwell's equations, Ampere's law, and displacement current.