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.