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Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies. Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents. They are named after the physicist and mathematician James Clerk Maxwell, who published an early form of those equations between 1861 and 1862. The equations have two major variants. The "microscopic" set of Maxwell's equations uses total charge and total current, including the complicated charges and currents in materials at the atomic scale; it has universal applicability but may be infeasible to calculate. The "macroscopic" set of Maxwell's equations defines two new auxiliary fields that describe large-scale behaviour without having to consider these atomic scale details, but it requires the use of parameters characterizing the electromagnetic properties of the relevant materials. The term "Maxwell's equations" is often used for other forms of Maxwell's equations. For example, space-time formulations are commonly used in high energy and gravitational physics. These formulations, defined on space-time rather than space and time separately, are manifestly〔Maxwell's equations in any form are compatible with relativity. These space-time formulations, though, make that compatibility more readily apparent.〕 compatible with special and general relativity. In quantum mechanics and analytical mechanics, versions of Maxwell's equations based on the electric and magnetic potentials are preferred. Since the mid-20th century, it has been understood that Maxwell's equations are not exact but are a classical field theory approximation to the more accurate and fundamental theory of quantum electrodynamics. In many situations, though, deviations from Maxwell's equations are immeasurably small. Exceptions include nonclassical light, photon-photon scattering, quantum optics, and many other phenomena related to photons or virtual photons. ==Formulation in terms of electric and magnetic fields== The powerful and most widely familiar form of Maxwell's equations, whose formulation is due to Oliver Heaviside, in the vector calculus formalism, is used throughout unless otherwise explicitly stated. Symbols in bold represent vector quantities, and symbols in ''italics'' represent scalar quantities, unless otherwise indicated. The equations introduce the electric field, , a vector field, and the magnetic field, , a pseudovector field, where each generally have time-dependence. The sources of these fields are electric charges and electric currents, which can be expressed as local densities namely charge density and current density . A separate law of nature, the Lorentz force law, describes how the electric and magnetic field act on charged particles and currents. A version of this law was included in the original equations by Maxwell but, by convention, is no longer. In the electric and magnetic field formulation there are four equations. Two of them describe how the fields vary in space due to sources, if any; electric fields emanating from electric charges in Gauss's law, and magnetic fields as closed field lines ''not due to magnetic monopoles'' in Gauss's law for magnetism. The other two describe how the fields "circulate" around their respective sources; the magnetic field "circulates" around electric currents and time varying electric fields in Ampère's law with Maxwell's addition, while the electric field "circulates" around time varying magnetic fields in Faraday's law. The precise formulation of Maxwell's equations depends on the precise definition of the quantities involved. Conventions differ with the unit systems, because various definitions and dimensions are changed by absorbing dimensionful factors like the speed of light . This makes constants come out differently. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Maxwell's equations」の詳細全文を読む スポンサード リンク
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