(Untitled) (Untitled)(Untitled) (Untitled)(Untitled) (Untitled)(Untitled) (Untitled)(Untitled)Examples

Language:enStatus: Standard
Term: Stokes theorem
Synonym1: circulation theorem
Definition: for a vector field U that is given at each point of a surface S limited by an oriented closed curve C, theorem stating that the surface integral over S of the rotation of the vector field U is equal to the circulation of this vector field along the curve C

S rot U e n dA= C Udr MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaapifabaacbeqcLb uacaWFYbGaa83Baiaa=rhaaSqaaKqzaeGaae4uaaWcbeqdcqGHRiI8 cqGHRiI8aOGaaGjbVlaahwfacqGHflY1caWHLbWaaSbaaSqaaKqzae GaaeOBaaWcbeaajugqbiaacsgakiaadgeacqGH9aqpdaWdvbqaaiaa hwfacqGHflY1caGGKbGaaCOCaaWcbaqcLbqacaqGdbaaleqaniablg H7rlabgUIiYdaaaa@53F1@

where endA is the vector surface element and dr is the vector line element

Note 1 to entry: The orientation of the surface S with respect to the curve C is chosen such that, at any point of C, the vector line element, the unit vector normal to S and defining its orientation, and the unit vector normal to these two vectors and oriented towards the exterior of the curve, form a right-handed or a left-handed trihedron according to space orientation.

Note 2 to entry: The Stokes theorem can be generalized to the n-dimensional Euclidean space.

Note 3 to entry: In magnetostatics, the Stokes theorem is applied to express that the magnetic flux through the surface S is equal to the circulation over C of the magnetic vector potential.

Publication date:2021-03
Internal notes:
CO remarks:
TC/SC remarks:
VT remarks: