Gauss' law

Gauss’ law (electrostatics) states that the electric flux through a closed surface is proportional to the total charge enclosed within that surface.

Differential form

$$\nabla \cdot \mathbf{E}=\frac{\rho }{{\epsilon }_0}$$

where
$\mathbf{E}(\mathbf{x},t)$	electric field, measured in volts per meter $\frac{\text{V}}{\text{m}}$
$\mathbf{x}$	position vector in three-dimensional space, typically expressed as $\mathbf{x}=(x,y,z)$ and measured in meters $\text{m}$
$t$	time, measured in seconds $\text{s}$
$\nabla \cdot$	divergence operator, which measures the net flux of a field out of an infinitesimal volume, and which when applied to $\mathbf{E}$ is: $\nabla \cdot \mathbf{E}=\frac{\partial }{\partial x}{E}_x+\frac{\partial }{\partial y}{E}_y+\frac{\partial }{\partial z}{E}_z,$ measured in volts per meter squared $\frac{\text{V}}{{\text{m}}^2}$
$\rho$	charge density, measured in coulombs per cubic meter $\frac{\text{C}}{{\text{m}}^3}$
${\epsilon }_0$	permittivity of free space, measured in farads per meter $(8.85\times 10^{-12}\frac{\text{F}}{\text{m}})$

Integral form

$${\oint }_S\mathbf{E}\cdot d\mathbf{A}=\frac{Q_{\text{enc}}}{{\epsilon }_0}$$

where
$S$	closed surface in three-dimensional space
${\int }_S$	surface integral which sums the contribution of the field $\mathbf{E}$ over the entire surface $S$
$d\mathbf{A}$	differential surface element, representing an infinitesimally small patch of the surface $S$
$Q_{\text{env}}$	total charge enclosed by the Gaussian surface, measured in coulombs $\text{C}$