% miko:type: atomic
% miko:title: Electric Potential
% miko:summary: A scalar potential whose gradient gives the electrostatic field.
% miko:tags: em
% miko:difficulty: undergrad
% miko:related: gauss-law, maxwell-equations
% miko:keywords: electrostatics, scalar potential, field

\documentclass{article}
\usepackage{amsmath}
\title{Electric Potential}
\begin{document}
\maketitle

\section{Definition}

In electrostatics,

$$
\mathbf E=-\nabla \phi.
$$

The potential difference is work per unit charge:

$$
\Delta \phi = -\int_A^B \mathbf E\cdot d\mathbf l.
$$

\section{Poisson Equation}

Combining with Gauss's law gives

$$
\nabla^2\phi=-\frac{\rho}{\varepsilon_0}.
$$

\end{document}
