Maxwell's equations

Faraday's law can be read as a statement about fields. An emf between two points is the work done per unit charge, so an induced emf means an electric field: a magnetic field changing in time produces an electric field.

The displacement current gives the matching statement: an electric field changing in time produces a magnetic field. Time-varying electric and magnetic fields generate each other.

This makes the laws of electricity and magnetism more symmetric, though not perfectly: no magnetic monopoles, sources of B analogous to electric charges, are known.

The four Maxwell equations in vacuum are Gauss's law ∮E·dA = Q/ε₀, Gauss's law for magnetism ∮B·dA = 0, Faraday's law ∮E·dl = −dΦB/dt, and the Ampere-Maxwell law ∮B·dl = μ₀ic + μ₀ε₀ dΦE/dt.

Together with the Lorentz force formula, these equations express all the basic laws of electromagnetism.

Their most important prediction is the electromagnetic wave: coupled electric and magnetic fields varying in time and travelling through space.

The predicted speed came out very close to 3 × 10⁸ m/s, the speed of light found from optical measurements. So light is an electromagnetic wave, and Maxwell's work unified electricity, magnetism and light.

Hertz demonstrated electromagnetic waves experimentally, and Marconi and others turned them into the technology of communication.