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Electromagnetic wave equation
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Electromagnetic wave equation : ウィキペディア英語版
Electromagnetic wave equation
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field or the magnetic field , takes the form:
:\begin
\left(c^2\nabla^2 - \frac \right) \mathbf &= \mathbf \\
\left(c^2\nabla^2 - \frac \right) \mathbf &= \mathbf
\end
where
: c = \frac{\sqrt {\mu_0\varepsilon_0}}
is the speed of light in a medium with permeability (0), and permittivity (0), and is the Laplace operator. In a vacuum, meters per second, which is the speed of light in free space.〔Current practice is to use to denote the speed of light in vacuum according to ISO 31. In the original Recommendation of 1983, the symbol was used for this purpose. See (NIST ''Special Publication 330'', Appendix 2, p. 45 )〕 The electromagnetic wave equation derives from Maxwell's equations. It should also be noted that in most older literature, is called the ''magnetic flux density'' or ''magnetic induction''.
==The origin of the electromagnetic wave equation==
] which when operated on by the divergence operator yields a vector. Since
:\begin
\nabla \cdot \mathbf &= 0\\
\nabla \cdot \mathbf &= 0
\end
then the first term on the right in the identity vanishes and we obtain the wave equations:
:\begin
\frac - c_0^2 \cdot \nabla^2 \mathbf &= 0\\
\frac - c_0^2 \cdot \nabla^2 \mathbf &= 0
\end
where
:c_0 = \frac
is the speed of light in free space.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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