[[Maxwell's equations]]
# Gauß's Law for Electric Flux
**Gauß's law** states that the number of field lines passing through the surface of a solid $\Omega$ (the electric [[flux]]) is proportional to the charge enclosed within.
$$
\begin{align*}
\Phi = \oiint_{\partial \Omega} \vab E \cdot d\vab a = \frac{Q_\text{enc}}{\epsilon_{0}} = \frac{1}{\epsilon_{0}} \iiint_{\Omega} \rho \,d\tau'
\end{align*}
$$
^Integral

Using [[Острогра́дский's divergence theorem]], we see
$$
\begin{align*}
\vab{\nabla} \cdot \vab E = \frac{\rho}{\epsilon_{0}}
\end{align*}
$$
^Differential

See also [[Gauß's law for diëlectrics]].

---
#state/tidy | #SemBr | #lang/en