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单词 MaxwellsEquations
释义

Maxwell’s equations


Maxwell’s equations are a set of four partial differential equationsMathworldPlanetmath first combined by James Clerk Maxwell. They may also be written as integral equationsMathworldPlanetmath. Two other important equations, the electromagnetic wave equation and the equation of conservation of charge, may be derived from them.

0.1 Notation

As this article considers merely the mathematical aspects of the equations, natural units have been used throughout. For their use in physics see any classical electromagnetism textbook.

𝐄=Electric field strength
𝐁=Magnetic flux density

0.2 Gauss’ Law of Electrostatics

𝐄=0
S𝐄d𝐒=0

0.3 Gauss’ Law of Magnetostatics

𝐁=0
S𝐁d𝐒=0

0.4 Faraday’s Law

Differential formMathworldPlanetmath

×𝐄=-𝐁t

Integral form

C𝐄d𝐥=-ddt(S𝐁d𝐒)

0.5 Ampère’s Law

Differential form

×𝐁=𝐄t

Integral form

C𝐁d𝐥=S𝐄td𝐒

0.6 Properties of Maxwell’s Equations

These four equations together have several interesting properties:

  • Lorentz invariance

  • The fields 𝐄 and 𝐁 may be Helmholtz decomposed into irrotational and solenoidal potentials. A gauge transformation in these variables does not affect the values of the fields.

TitleMaxwell’s equations
Canonical nameMaxwellsEquations
Date of creation2013-03-22 17:51:34
Last modified on2013-03-22 17:51:34
Ownerinvisiblerhino (19637)
Last modified byinvisiblerhino (19637)
Numerical id28
Authorinvisiblerhino (19637)
Entry typeDefinition
Classificationmsc 35Q60
Classificationmsc 78A25
Related topicPartialDifferentialEquation
DefinesFaraday’s Law
DefinesAmpere’s Law
DefinesGauss’ Law of Electrostatics
DefinesGauss’ Law of Magnetostatics
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