At class, I have been proposed the following exercise:
Consider the vector field $$\mathbf{f}(x,y,z) = (y-z,z-x,x-y).$$ Calculate the flux of $\mathbf{f}$ through the surface $$S = \{x^2+y^2+z^2 = 2ax,\, x^2+y^2 \leq 2bx,\,z \geq 0,\,b > a >0\},$$ which is oriented upward, using Stokes' Theorem.
My first idea was to use Gauss' Theorem. However, I am specifically asked to use Stokes' Theorem to calculate the flux.
My question is: Which application of Stokes' Theorem should I use then?
Perhaps it is not immediate.
Any help would be greatly appreciated.