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IEVref: | 102-05-30 | ID: | |

Language: | en | Status: Standard | |

Term: | divergence theorem | ||

Synonym1: | Gauss theorem | ||

Synonym2: | Ostrogradsky theorem | ||

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Definition: | for a vector field 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 SU$\underset{\text{V}}{\iiint}\mathrm{div}\text{\hspace{0.17em}}U}dV={\displaystyle \underset{\text{S}}{\u222f}U}\cdot {e}_{\text{n}}dA$ where d Note 1 to entry: The divergence theorem can be generalized to the 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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$\underset{\text{V}}{\iiint}\mathrm{div}\text{\hspace{0.17em}}U}dV={\displaystyle \underset{\text{S}}{\u222f}U}\cdot {e}_{\text{n}}dA$

where d*V* is the volume element and *e*_{n}d*A* 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".