What is the practical application of Stokes theorem?

Physical applications of Strokes’ theorem. Sufficient conditions for a vector field to be conservative. Stokes’ theorem gives a relation between line integrals and surface integrals. Depending upon the convenience, one integral can be computed interms of the other.

Which is necessary to apply Stokes theorem?

If one coordinate is constant, then curve is parallel to a coordinate plane. (The xz-plane for above example). For Stokes’ theorem, use the surface in that plane. For our example, the natural choice for S is the surface whose x and z components are inside the above rectangle and whose y component is 1.

What does Stokes theorem compute in context of engineering applications?

Stokes’ theorem translates between the flux integral of surface S to a line integral around the boundary of S. Therefore, the theorem allows us to compute surface integrals or line integrals that would ordinarily be quite difficult by translating the line integral into a surface integral or vice versa.

In which case the Stokes theorem is not applicable?

Stokes theorem does not always apply. The first condition is that the vector field, →A, appearing on the surface integral side must be able to be written as →∇×→F, where →F would either have to be found or may be given to you. If →F cannot be found, then Stokes theorem cannot be used.

How do you prove Green theorem?

= ∫ b M(x, c) dx + M(x, d) dx = M(x, c) − M(x, d) dx. So, for a rectangle, we have proved Green’s Theorem by showing the two sides are the same. Theorem on a sum of rectangles. Since any region can be approxi mated as closely as we want by a sum of rectangles, Green’s Theorem must hold on arbitrary regions.

What is the physical significance of Stokes theorem?

Stoke’s Theorem relates a surface integral over a surface to a line integral along the boundary curve. In fact, Stokes’ Theorem provides insight into a physical interpretation of the curl.

Why is Stokes theorem true?

Stokes’ theorem allows us to do even more. We don’t have to leave the curve C sitting in the xy-plane. We can twist and turn C as well. If S is a surface whose boundary is C (i.e., if C=∂S), it is still true that ∫CF⋅ds=∬ScurlF⋅dS.