Electrodynamics

Electrodynamics is the branch of physics that describes how electric charges and currents interact with electric and magnetic fields, and how those fields propagate and interact with matter. In classical physics, the subject is governed by Maxwell's equations, which relate charges and currents to the electric and magnetic fields. The equations in differential form are: Gauss's law ∇·E = ρ/ε0, Gauss's law for magnetism ∇·B = 0, Faraday's law of induction ∇×E = -∂B/∂t, and the Ampère–Maxwell law ∇×B = μ0 J + μ0 ε0 ∂E/∂t. Together with the Lorentz force law F = q(E + v×B), these equations describe the motion of charges and the evolution of fields.

Electromagnetic waves arise from these equations and propagate through space at the speed of light in vacuum, c = 1/√(ε0 μ0). The energy and momentum carried by the fields are described by the Poynting vector S = (1/μ0) E×B and by the energy density u = (ε0 E^2 + B^2/μ0)/2. The theory can be expressed compactly in relativistic form using the electromagnetic field tensor F^{μν}, and in matter through constitutive relations that relate E and B to D and H, accounting for absorption, dispersion, and polarization.

Historically, electrodynamics arose from Faraday’s experiments and was formulated into a complete theory by James Clerk Maxwell in the 19th century. It underpins electric circuits, radio and optics, and many areas of physics, and it provides the classical framework preceding quantum electrodynamics for light–matter interactions.