## Maxwell's equations |

Part of a series of articles about |

**Maxwell's equations** are a set of

The equations have two major variants. The microscopic Maxwell equations have universal applicability, but are unwieldy for common calculations. They relate the electric and magnetic fields to total charge and total current, including the complicated charges and currents in materials at the

The term "Maxwell's equations" is often also used for equivalent alternative formulations. Versions of Maxwell's equations based on the ^{[note 1]} In fact,

Since the mid-20th century, it has been understood that Maxwell's equations are not exact, but a

- conceptual descriptions
- formulation in terms of electric and magnetic fields (microscopic or in vacuum version)
- relationship between differential and integral formulations
- charge conservation
- vacuum equations, electromagnetic waves and speed of light
- macroscopic formulation
- alternative formulations
- relativistic formulations
- solutions
- overdetermination of maxwell's equations
- maxwell equations as the classical limit of qed
- variations
- see also
- notes
- references
- historical publications
- further reading
- external links

** Gauss's law** describes the relationship between a static

** Gauss's law for magnetism** states that there are no "magnetic charges" (also called

The ** Maxwell–Faraday** version of

The dynamically induced electric field has closed field lines similar to a magnetic field, unless superposed by a static (charge induced) electric field. This aspect of

** Ampère's law with Maxwell's addition** states that magnetic fields can be generated in two ways: by

Maxwell's addition to Ampère's law is particularly important: it makes the set of equations mathematically consistent for non static fields, without changing the laws of Ampere and Gauss for static fields.^{[2]} However, as a consequence, it predicts that a changing magnetic field induces an electric field and vice versa.^{[1]}^{[3]} Therefore, these equations allow self-sustaining "

The speed calculated for electromagnetic waves, which could be predicted from experiments on charges and currents,^{[note 2]} exactly matches the *is* one form of

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