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**Maxwell's equations** are four equations that
James Clerk Maxwell created and/or refined that
describe the behavior and interaction of
electricity and magnetism. This description
includes the conditions for propagating waves,
i.e., electromagnetic waves,
explaining electromagnetic radiation, including visible light.

The equations are (in their differential-equation form):

Gauss's law | ∇ · E = 4πρ | Electric field lines begin and end at charged particles. |

Gauss's law for magnetism | ∇ · B = 0 | Magnetic field lines don't end: they form circuits. If magnetic monopoles existed, a non-zero value could be on the right side of this equation. |

Maxwell-Faraday equation | ∇ × E = - (1/c) ∂B/∂t | The magnetic field is shifting when/where the electric field curls around. |

Ampere's law | ∇ × B = (1/c)(4πJ + ∂E/∂t) | When/where the magnetic field curls around, you get electric current, or a shift in the electric field, or some of each. |

- E - electric field.
- B - magnetic field (magnetic flux density).
- J - electric current density.
- ρ - electric charge density.
- t - time.
- c - speed of light in a vacuum.

CMB polarization

Coulomb's law

Lorentz force

magnetic flux density (B)

magnetic induction

mathematical field

magnetohydrodynamics (MHD)

Mie scattering

photon

telegrapher's equations

Theory of Everything (TOE)