IEVref: 102-05-30 ID: Language: en Status: Standard Term: divergence theorem Synonym1: Gauss theorem Synonym2: Ostrogradsky theorem Synonym3: Symbol: Definition: 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 $\underset{\text{V}}{\iiint }\mathrm{div}\text{\hspace{0.17em}}UdV=\underset{\text{S}}{∯}U\cdot {e}_{\text{n}}dA$ where dV is the volume element and endA is the vector surface elementNote 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". Publication date: 2017-07 Source: Replaces: 102-05-30:2007-08 Internal notes: CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: