For thermodynamic relations, see Maxwell relations. For the history of the equations, see History of Maxwell’s equations. For a general description of electromagnetism, zangwill modern electrodynamics pdf Electromagnetism. Maxwell’s equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.

They underpin all electric, optical and radio technologies, including power generation, electric motors, wireless communication, cameras, televisions, computers etc. Maxwell’s equations describe how electric and magnetic fields are generated by charges, currents, and changes of each other.

One important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at the speed of light. Known as electromagnetic radiation, these waves may occur at various wavelengths to produce a spectrum from radio waves to γ-rays. The equations are named after the physicist and mathematician James Clerk Maxwell, who between 1861 and 1862 published an early form of the equations, and first proposed that light is an electromagnetic phenomenon. The equations have two major variants.

The microscopic Maxwell equations have universal applicability, but are unwieldy for common calculations. They relate the electric and magnetic fields to total charge and total current, including the complicated charges and currents in materials at the atomic scale. The “macroscopic” Maxwell equations define two new auxiliary fields that describe the large-scale behaviour of matter without having to consider atomic scale details.

However, their use requires experimentally determining parameters for a phenomenological description of the electromagnetic response of materials. The term “Maxwell’s equations” is often used for equivalent alternative formulations.

Versions of Maxwell’s equations based on the electric and magnetic potentials are preferred for explicitly solving the equations as a boundary value problem, analytical mechanics, or for use in quantum mechanics. In fact, Einstein developed special and general relativity to accommodate the absolute speed of light that drops out of the Maxwell equations with the principle that only relative movement has physical consequences.

Since the mid-20th century, it has been understood that Maxwell’s equations are not exact, but a classical field theory approximation of some aspects of the fundamental theory of quantum electrodynamics, although some quantum features, such as quantum entanglement, are completely absent and in no way approximated. For example, quantum cryptography has no approximate version in Maxwell theory. In many situations, though, deviations from Maxwell’s equations are immeasurably small. In the electric and magnetic field formulation there are four equations.