Derive wave equation for z- component of electric field of an electromagnetic wave
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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:
vph2∇2∂2∂t2 E 0 vph2∇2∂2∂t2 B 0
where
vph 1με
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 = 299,792,458 meters per second, a fundamental physical constant.[1] The electromagnetic wave equation derives from Maxwell's equations. It should also be noted that in most older literature, B is called the magnetic flux density or magnetic induction.
vph2∇2∂2∂t2 E 0 vph2∇2∂2∂t2 B 0
where
vph 1με
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 = 299,792,458 meters per second, a fundamental physical constant.[1] The electromagnetic wave equation derives from Maxwell's equations. It should also be noted that in most older literature, B is called the magnetic flux density or magnetic induction.
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