Electromagnetic wave equation
Partial differential equation used in physics / From Wikipedia, the free encyclopedia
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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 E or the magnetic field B, takes the form:
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where
is the speed of light (i.e. phase velocity) in a medium with permeability μ, and permittivity ε, and ∇2 is the Laplace operator. In a vacuum, vph = c0 = 299792458 m/s, a fundamental physical constant.[1] The electromagnetic wave equation derives from Maxwell's equations. In most older literature, B is called the magnetic flux density or magnetic induction. The following equations
predicate that any electromagnetic wave must be a transverse wave, where the electric field E and the magnetic field B are both perpendicular to the direction of wave propagation.