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

## Physical Law

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

where:

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

## Also presented as

This equation can also be seen presented as:

$\nabla \times \mathbf H = \mathbf J + \dfrac {\partial \mathbf D} {\partial t}$

where:

$\mathbf D = \varepsilon_0 \mathbf E$ denotes the electric displacement field
$\mathbf H = \dfrac 1 {\mu_0} \mathbf B$ denotes the magnetic field strength

## Source of Name

This entry was named for James Clerk Maxwell and André-Marie Ampère.