Stokes theorem When a vector field intersects a non-closed surface S bounded by a contour C as shown
in Figure 1.7, and the sense of the contour is chosen so that it is related to the sense of
the surface area by the right hand rule, it has been shown by Stokes that
Notice that the line integral is a closed one, but the surface integral is not closed.
Stokes' theorem may be put into words as stating that the circulation of a vector field
around a contour bounding a surface is equal to the flux of the curl of that field passing
through that surface.
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