Electromagnetic wave

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

The spectrum of electromagnetic waves has an extremely wide range from radio waves, micro waves, TeraHertz radiation, infrared (IR) radiation, visible light, ultraviolett (UV) light, far UV radiation, soft X-rays, hard X-rays and <math>\gamma</math>-radiation.

Electromagnetic waves are well described by the classical laws of electricity and magnetism, known as Maxwell's equations:

Name	Partial Differential Equations	Integral Equations
Gauss's Law of Conservation:	<math>\nabla \cdot \mathbf{D} = \rho</math>	<math>\oint_S \mathbf{D} \cdot \mathrm{d}\mathbf{A} = \int_V \rho\, \mathrm{d}V</math>
Gauss' Law Of Magnetism:	<math>\nabla \cdot \mathbf{B} = 0</math>	<math>\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0</math>
Faraday's Law of Induction:	<math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}</math>	<math>\oint_C \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \int_S \frac{\partial\mathbf{B}}{\partial t} \cdot \mathrm{d} \mathbf{A}</math>
Ampère's Law of Circulation	<math>\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}} {\partial t}</math>	<math>\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}</math>

where B denotes the magnetic field, E denotes the electric field, H denotes the auxiliary magnetic field, J denotes the free current density, and <math>\rho</math> denotes the free electric charge density.

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

<math>\mathrm{d}\bold{F}=0</math>

<math>\mathrm{d} * {\bold{F}}=\bold{J}</math>

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.