Gauss' law (electrostatics)

In physics, more specifically in electromagnetism, Gauss' law is a theorem concerning a surface integral of an electric field. In vacuum it takes the form (in SI units):

$\iint _{\mathrm {closed} \atop \mathrm {surface} }\mathbf {E} \cdot d\mathbf {S} ={\frac {Q_{\mathrm {tot} }}{\epsilon _{0}}}.$

Here dS is an vector with length dS, the area of an infinitesimal surface element, and direction perpendicular to the surface element dS. The vector E is the electric field at the position dS, the dot indicates an inner product between the vectors E and dS. The double integral is over a closed surface that envelops a total electric charge Q_tot. The constant ε₀ is the vacuum permeability. The law is called after the German mathematician Carl Friedrich Gauss.