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Maxwell's equations
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(Definition)
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Maxwell's equations are a set of four partial differential equations first combined by James Clerk Maxwell. They may also be written as integral equations. Two other important equations, the electromagnetic wave equation and the equation of conservation of charge, may be derived from them.
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. $$ \mathbf{E} = \mbox{Electric field strength} $$ $$ \mathbf{B} = \mbox{Magnetic flux density} $$
$$ \nabla \cdot \mathbf{E} = 0 $$ $$ \oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{S} = 0 $$
$$ \nabla \cdot \mathbf{B} = 0 $$ $$ \oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{S} = 0 $$
Differential form $$ \nabla \times \mathbf{E} = -\frac{ \partial \mathbf{B}}{\partial t} $$ Integral form $$ \oint_{C} \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \frac{\mathrm{d}}{\mathrm{d} t} \left( \int_{S} \mathbf{B} \cdot \mathrm{d}\mathbf{S} \right) $$
Differential form $$ \nabla \times \mathbf{B} = \frac{ \partial \mathbf{E}}{\partial t} $$ Integral form $$ \oint_C \mathbf{B} \cdot \mathrm{d}\mathbf{l} = \int_S \frac{\partial \mathbf{E}}{\partial t} \cdot \mathrm{d} \mathbf{S} $$
These four equations together have several interesting properties:
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"Maxwell's equations" is owned by invisiblerhino.
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Cross-references: variables, transformation, gauge, potentials, solenoidal, irrotational, fields, properties, integral, differential form, units, wave equation, equations, integral equations, partial differential equations
There are 4 references to this entry.
This is version 25 of Maxwell's equations, born on 2008-02-26, modified 2008-04-21.
Object id is 10336, canonical name is MaxwellsEquations.
Accessed 3678 times total.
Classification:
| AMS MSC: | 35Q60 (Partial differential equations :: Equations of mathematical physics and other areas of application :: Equations of electromagnetic theory and optics) | | | 78A25 (Optics, electromagnetic theory :: General :: Electromagnetic theory, general) |
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Pending Errata and Addenda
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