| 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|
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.