| for a vector field U that is given at each point of a three-dimensional domain V limited by a closed surface S having an orientation towards exterior, theorem stating that the volume integral over V of the divergence of the field U is equal to the flux of this field through the surface S|
where dV is the volume element and endA is the vector surface element
Note 1 to entry: The divergence theorem can be generalized to the n-dimensional Euclidean space.
Note 2 to entry: In electrostatics, the divergence theorem is applied to express that the electric flux through a closed surface is equal to the total electric charge in the domain enclosed by the surface. It is then called "Gauss law".