# Maxwell's Equations

## Physical Laws

### Gauss's Law

$\nabla \cdot \mathbf E = \dfrac \rho {\varepsilon_0}$

### Gauss's Law for Magnetism

$\nabla \cdot \mathbf B = 0$

$\nabla \times \mathbf E = -\dfrac {\partial \mathbf B} {\partial t}$

### Ampère's Law with Maxwell's Addition

$\nabla \times \mathbf B = \mu_0 \paren {\mathbf J + \varepsilon_0 \dfrac {\partial \mathbf E} {\partial t} }$

where:

$\nabla \cdot$ denotes the divergence operator
$\nabla \times$ denotes the curl operator
$\dfrac \partial {\partial t}$ denotes the partial derivative with respect to time.
$\mathbf E$ denotes the electric field strength
$\mathbf B$ denotes the magnetic flux density
$\mathbf J$ denotes the electric current
$\rho$ denotes volume charge density
$\varepsilon_0$ denotes the vacuum permittivity
$\mu_0$ denotes the vacuum permeability.

## Also known as

Maxwell's equations are also known as Maxwell's laws.

## Source of Name

This entry was named for James Clerk Maxwell.