# Gauss's Law

## Table of Contents

$$ \oiint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon_0} $$

Where

- The left side is a surface integral of the electric field \(\vec{E}\) over a closed surface \(\vec{A}\), and
- \(Q_{enc}\) is the charge enclosed by the surface, and
- \(\epsilon_0\) is the permittivity of free space.

## Differential form #

Gauss’s law can also be written in differential form:

$$ \nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0} $$

Where

- The left side is the divergence of the electric field \(\vec{E}\), and
- \(\rho\) is the charge density.