When can you use Stokes theorem?

Stokes’ theorem can be used to turn surface integrals through a vector field into line integrals. This only works if you can express the original vector field as the curl of some other vector field. Make sure the orientation of the surface’s boundary lines up with the orientation of the surface itself.

What does Stokes theorem measure?

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.

What does DS mean in Stokes theorem?

C. v · dr = ∫ C. v ·T ds is the circulation of v around C. Stokes’ Theorem =⇒ Circulation = ∫∫

What happens if Stokes theorem is applied to a closed surface?

closed surfaces A surface S⊂R3 is said to be closed if it has no (Stokes) boundary. An example of such a surface is the unit sphere S={(x,y,z)∈R3:x2+y2+z2=1},n oriented outwards.

Which of the following is correct expression for Stokes theorem?

dl = ∫∫ Curl (A). ds is the expression for Stoke’s theorem. It is clear that the theorem uses curl operation.

Why do we use Stokes theorem?

Stokes’ theorem can be used to transform a difficult surface integral into an easier line integral, or a difficult line integral into an easier surface integral. Through Stokes’ theorem, line integrals can be evaluated using the simplest surface with boundary C.

Can Stokes theorem be used for closed surface?

What is C in Stokes theorem?

Stokes’ Theorem Formula The Stoke’s theorem states that “the surface integral of the curl of a function over a surface bounded by a closed surface is equal to the line integral of the particular vector function around that surface.” Where, C = A closed curve. S = Any surface bounded by C.