Maxwell's equations

Four coupled equations describe how electric and magnetic fields arise from charge and current and change over time. Together they predict electromagnetic waves and unify electricity, magnetism, and optics.

Gauss's law for electricity: Electric charge is the source or sink of electric flux through a closed surface. It specifies how charge determines the divergence of the electric field.
Electric charge: A fundamental property of matter that produces and responds to electromagnetic interactions. Charge density appears as the source in Gauss's law for electricity.
James Clerk Maxwell: A Scottish physicist whose work unified electricity, magnetism, and light in classical field theory. He assembled the electromagnetic laws and introduced the displacement-current term.
Radio antenna: A conductor or array that transmits or receives electromagnetic waves. Antenna radiation follows from time-varying currents and fields governed by the equations.
Coulomb's law: A law giving the electrostatic force between point charges in terms of their separation and charges. It describes static electric interactions, while Maxwell's equations also cover changing fields.
Gauss's law for magnetism: The net magnetic flux through any closed surface is zero. It expresses the absence of observed magnetic monopoles in the equations.
Electric current: The rate at which electric charge flows through a surface. Current density sources magnetic-field circulation in the Ampère–Maxwell law.
Michael Faraday: An English experimental physicist whose discoveries include electromagnetic induction. His induction law became one of the equations Maxwell brought together.
Waveguide: A structure that confines and directs electromagnetic waves along a path. Its supported modes are solutions of Maxwell's equations with boundary conditions.
Biot–Savart law: A law calculating the magnetic field produced by steady electric currents. It applies to steady-current settings rather than the full time-dependent field framework.

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