% miko:type: atomic
% miko:title: Ampere-Maxwell Law
% miko:summary: Magnetic circulation is sourced by current and changing electric flux.
% miko:tags: em
% miko:difficulty: undergrad
% miko:related: maxwell-equations, faraday-law, wave-equation
% miko:keywords: displacement current, magnetic field, curl

\documentclass{article}
\usepackage{amsmath}
\title{Ampere-Maxwell Law}
\begin{document}
\maketitle

\section{Differential Form}

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

\section{Displacement Current}

The term

$$
\mu_0\varepsilon_0\frac{\partial\mathbf E}{\partial t}
$$

is Maxwell's correction. It makes charge conservation compatible with the field
equations and permits electromagnetic waves.

\end{document}
