Let C be the ellipse contained in the xy plane whose equation is , oriented clockwise. The force field F described by , moves a particle along C in the same direction as the curve orientation, performing a W job. C as the surface boundary S: (with ascending orientation, that is, the component in the z direction equal to 1) and assuming , we can state what:
a) It is not necessary to apply Stokes' Theorem, as C is a closed curve and therefore .
b) Inverting the orientation of the surface S, we can apply Stokes' Theorem and conclude that
c) We can apply Stokes' Theorem and conclude that
d) We can apply Stokes' Theorem and conclude that