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: where endA is the vector surface element and dr is the vector line element NOTE 1 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 The Stokes theorem can be generalized to the n-dimensional Euclidean space. NOTE 3 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 121-11-24.
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