Electromagnetic wave equation

Partial differential equation used in physics

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: ( v p h 2 ∇ 2 − ∂ 2 ∂ t 2) E = 0 ( v p h 2 ∇ 2 − ∂ 2 ∂ t 2) B = 0 {\displaystyle {\begin{aligned}\left(v_{\mathrm {ph} }^{2}\nabla ^{2}-{\frac {\partial ^{2}}{\partial t^{2}}}\right)\mathbf {E} &=\mathbf {0} \\\left(v_{\mathrm {ph} }^{2}\nabla ^{2}-{\frac {\partial ^{2}}{\partial t^{2}}}\right)\mathbf {B} &=\mathbf {0} \end{aligned}}} where v p h = 1 μ ε {\displaystyle v_{\mathrm {ph} }={\frac {1}{\sqrt {\mu \varepsilon }}}} is the speed of light (i.e.

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