IEVref: 102-05-31 ID: Language: en Status: Standard Term: Stokes theorem Synonym1: circulation theorem Synonym2: Synonym3: Symbol: 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 field U is equal to the circulation of this field along the curve C$\underset{\text{S}}{\iint }\mathrm{rot}\text{\hspace{0.17em}}U\cdot {e}_{\text{n}}dA=\underset{\text{C}}{\oint }U\cdot dr$ where endA is the vector surface element and dr is the vector line elementNote 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. This circulation defines the linked flux. See IEV 121-11-24. Publication date: 2008-08 Source: Replaces: Internal notes: 2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: