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IEVref:102-05-30ID:
Language:enStatus: 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

V divU dV= S U e n dA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaapmfabaqcLbuaca GGKbGaaiyAaiaacAhakiaahwfaaSqaaKqzaeGaaeOvaaWcbeqdcqGH RiI8cqGHRiI8cqGHRiI8aKqzafGaaiizaOGaamOvaiabg2da9maapy fabaGaaCyvaaWcbaqcLbqacaqGtbaaleqaniablkH7slabgUIiYlab gUIiYdGccqGHflY1caWHLbWaaSbaaSqaaiaab6gaaeqaaKqzafGaai izaOGaamyqaaaa@575B@

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".


Publication date:2017-07
Source:
Replaces:102-05-30:2007-08
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