% miko:type: complete
% miko:title: Complete Electromagnetism
% miko:summary: A field-first path through electrostatics, induction, and electromagnetic waves.
% miko:tags: em
% miko:difficulty: undergrad
% miko:related: maxwell-equations, gauss-law, faraday-law, wave-equation
% miko:keywords: Maxwell equations, fields, waves

\documentclass{article}
\usepackage{amsmath}
\title{Complete Electromagnetism}
\begin{document}
\maketitle

\section{Field View}

Electromagnetism is most compactly written in terms of fields $\mathbf E$ and
$\mathbf B$.

\section{Maxwell Equations}

The four equations organize sources, constraints, and dynamics:

$$
\nabla\cdot\mathbf E=\frac{\rho}{\varepsilon_0},
\qquad
\nabla\cdot\mathbf B=0,
$$

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

\section{Waves}

In vacuum these imply electromagnetic waves moving at $c$.

\end{document}
