Understanding the Relationship Between Surface & Line Integrals

[wasi-uz-zaman]

hi experts
as far I know the stokes theorem relates surface integral to line integral - but i am confuse how surface integral if represent area gets equal to length as represented by line integral.

 

[Citan Uzuki]

If the vector field F has units u, then the integral of F over a curve has units u*length. Stokes's theorem says that this is the same as the integral of ∇×F over a surface. ∇×F has units of u/length (since each of the partial derivatives does), so the integral of that over a surface has units u/length * length^2 = u*length - just as the integral of F over a curve does. Does that help?

 

[wasi-uz-zaman]

great - thanks a lot