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:	<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, and * is the Hodge star operator.