Let S S be the side of the cylinder x 2 + y 2 = 4 ,

Let $S$ be the side of the cylinder $x^2+y^2=4,0\le z\le 2$ (not including the top and bottom of the cylinder). Use Stokes' Theorem to compute the flux of $F(x,y,z)=⟨0,y,-z⟩$ through $S$ (with outward-pointing normal) by finding a vector potential $A$ such that $\mathrm{curl}\left(A\right)=F$.