Electromagnetic wave

A transverse wave composed of an oscillating electrical field and a magnetic field that oscillates perpendicular to the electric field.

Electromagnetic waves was predicted by the classical laws of electricity and magnetism, known as Maxwell's equations:

Name	Partial Differential Equations	Integral Equations
Gauss's Law of Conservation:	$\nabla \cdot \mathbf {D} =\rho$	$\oint _{S}\mathbf {D} \cdot \mathrm {d} \mathbf {A} =\int _{V}\rho \,\mathrm {d} V$
Gauss' Law Of Magnetism:	$\nabla \cdot \mathbf {B} =0$	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0}
Faraday's Law of Induction:	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}}	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A}}
Ampère's Law of Circulation	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}}	Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \oint_C \mathbf{H} \cdot \mathrm{d}\mathbf{l} = \int_S \mathbf{J} \cdot \mathrm{d} \mathbf{A} + \int_S \frac{\partial\mathbf{D}}{\partial t} \cdot \mathrm{d} \mathbf{A}}

where B denotes the magnetic field, E denotes the electric field, H denotes the auxiliary magnetic field, J denotes the free current density, and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho} denotes the free electric charge density.

In the language of Exterior Calculus, Maxwell's equations can be rewritten much more compactly as:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{d}\bold{F}=0}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{d} * {\bold{F}}=\bold{J}}

where d is exterior derivative operator, * is the Hodge star operator, and F is the force exerted upon a charged particle by the electric field and magnetic field.