Gauss's Law
Imagine any closed surface in 3D physical space. The net static electric flux through that surface is the two-dimensional integral of the scalar product E.dA of the electric vector E at the area element dA with the area element. The direction of the vector area element is normal to the actual infinitesimal element of area of the surface. The total charge inside the surface is the three dimensional integral of the charge density multiplied by volume element dV.
Gauss's law in integral form says that the total electric flux through the closed surface is proportional to the enclosed electric charge. In local or differential form, Gauss's law says that the divergence of the electric field at a point in space is proportional to the charge density at that point.
