## Maxwell's equations |

part of a series of articles about electromagnetism electricity magnetism

**maxwell's equations**are a set of coupled that, together with thepartial differential equations law, form the foundation oflorentz force , classicalclassical electromagnetism , andoptics . the equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors,electric circuits communication, lenses, radar etc. maxwell's equations describe howwireless andelectric are generated bymagnetic fields ,charges , and changes of the fields.currents ^{[note 1]}an important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at a constant speed () in a vacuum. known asc , these waves may occur at various wavelengths to produce aelectromagnetic radiation of light fromspectrum toradio waves . the equations are named after the physicist and mathematicianγ-rays , who published an early form of the equations that included the lorentz force law between 1861 and 1862. maxwell first used the equations to propose that light is an electromagnetic phenomenon.james clerk maxwell 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

. the "macroscopic" maxwell equations define two new auxiliary fields that describe the large-scale behaviour of matter without having to consider atomic scale charges and quantum phenomena like spins. however, their use requires experimentally determined parameters for a phenomenological description of the electromagnetic response of materials.atomic scale the term "maxwell's equations" is often also used for

equivalent alternative formulations . versions of maxwell's equations based on the andelectric are preferred for explicitly solving the equations as amagnetic potentials ,boundary value problem , or for use inanalytical mechanics . thequantum mechanics (oncovariant formulation rather than space and time separately) makes the compatibility of maxwell's equations withspacetime special relativity .manifest , commonly used inmaxwell's equations in curved spacetime andhigh energy , are compatible withgravitational physics .general relativity ^{[note 2]}in fact, developed special and general relativity to accommodate the invariant speed of light, a consequence of maxwell's equations, with the principle that only relative movement has physical consequences.einstein the publication of the equations marked the

of previously described phenomena: magnetism, electricity, light and associated radiation. since the mid-20th century, it has been understood that maxwell's equations are not exact, but aunification limit of the fundamental theory ofclassical .quantum electrodynamics - conceptual descriptions
- formulation in terms of electric and magnetic fields (microscopic or in vacuum version)
- relationship between differential and integral formulations
- charge conservation
- vacuum equations, electromagnetic waves and speed of light
- macroscopic formulation
- alternative formulations
- relativistic formulations
- solutions
- overdetermination of maxwell's equations
- maxwell's equations as the classical limit of qed
- variations
- see also
- notes
- references
- historical publications
- further reading
- external links

**Maxwell's equations** are a set of coupled ^{[note 1]} An important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at a constant speed (* c*) in a vacuum. Known as

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

The term "Maxwell's equations" is often also used for equivalent alternative formulations. Versions of Maxwell's equations based on the ^{[note 2]} In fact,

The publication of the equations marked the