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Stokes’ Theorem

Stokes’ theorem combines the ideas of Green’s theorem with the curl of a vector field. Green’s theorem applies only to two-dimensional vector fields and to regions in the two-dimensional plane. Stokes’ theorem generalises Green’s theorem to three dimensions.

This theorem states that the line integral of a vector around a closed path is equal to the surface integral of the normal component of its curl over the surface bounded by the path.
Description: 74732.png
where S is the surface enclosed by the path L. The positive direction of Description: 74720.png is related to the positive sense of defining L according to the right-hand rule.

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