Maxwell's equations in SI units in vacuum
Name Differential form Integral form Gauss's law (in vacuum) Gauss's law for magnetism Faraday's law of induction Ampère's circuital law
(with Maxwell's correction)
Descriptions of each lawEdit
Gauss's law states that the total electric flux passing through any charged surface is proportional to the charge within the surface. In other words, the divergence at any point is equal to charge density over the permittivity.
Gauss's law for magnetismEdit
The magnetic flux passing through any closed surface is zero, or the divergence is zero everywhere. This means there can be no magnetic monopoles (magnets with only a north or a south pole).
Faraday's law of inductionEdit
Ampère's circuital lawEdit
The line integral of a magnetic field around any closed loop is proportional to the current flowing around the loop and the change in electric flux through the loop (the latter part is called Maxwell's addition). It is related to the speed of light (c) by the formula