[[Maxwell's equations in materials]]
# Electric displacement

The **electric displacement** is an auxiliary field defined as
$$
\begin{align*}
\vab D = \epsilon_{0} \vab E + \vab P
\end{align*}
$$
where $\vab E$ is the [[electric field]] and $\vab P$ is the [[Electric dipole moment|electric polarization density]].
$\vab D$ satisfies [[Gauß's law for diëlectrics]] which is analogous to Gauß's law satisfied by $\vab E$,
however unlike $\vab E$ its curl does not in general vanish ($\vab{\nabla} \times \vab D = \vab{\nabla} \times \vab P$).

## Linear media
In the special case of a [[Linear diëlectric]]
$$
\begin{align*}
\vab D = \epsilon \vab E
\end{align*}
$$

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