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Maxwell's equations are a set of four partial differential equations describing classical electromagnetism. They are:

Maxwell's equations in SI units in vacuum
(for reference)
Name Differential form Integral form
Gauss's law (in vacuum) $\nabla \cdot \vec{\mathbf{E}} = \frac {\rho} {\epsilon_0}$ ${\scriptstyle S }$ $\vec{\mathbf{E}} \cdot \ \mathrm{d} \vec{s} = \frac{q}{\epsilon_0}$
Gauss's law for magnetism $\nabla \cdot \vec{\mathbf{B}} = 0$ ${\scriptstyle S }$ $\vec{\mathbf{B}} \cdot \ \mathrm{d} \vec{s} = 0$
Faraday's law of induction $\nabla \times \vec{\mathbf{E}} = -\frac{\partial \vec{\mathbf{B}}} {\partial t}$ $\oint \vec{\mathbf{E}} \cdot d \vec{r} = - \frac{d}{dt} \iint \vec{\mathbf{B}} \cdot d \vec{s}$
Ampère's circuital law
(with Maxwell's correction)
$\nabla \times \vec{\mathbf{B}} = \mu_0 \ \vec{\mathbf{J}} + \frac{1}{c^2} \ \frac{\partial \vec{\mathbf{E}}} {\partial t}\$ $\oint \vec{\mathbf{B}} \cdot d \vec{r} = \mu_0 \iint \vec{\mathbf{J}} \cdot d \vec{s} + \frac{1}{c^2} \iint \vec{\mathbf{E}} \cdot d \vec{s}$

## Descriptions of each lawEdit

### Gauss's 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).

$c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$