% miko:type: atomic
% miko:title: Faraday's Law
% miko:summary: A changing magnetic field induces a circulating electric field.
% miko:tags: em
% miko:difficulty: undergrad
% miko:related: maxwell-equations, wave-equation, complete-electromagnetism
% miko:keywords: induction, curl, magnetic flux

\documentclass{article}
\usepackage{amsmath}
\title{Faraday's Law}
\begin{document}
\maketitle

\section{Integral Form}

$$
\oint_{\partial S}\mathbf E\cdot d\mathbf l =
-\frac{d}{dt}\int_S \mathbf B\cdot d\mathbf A.
$$

\section{Differential Form}

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

The minus sign encodes Lenz's law.

\end{document}
