Circulation and flux For the following vector fields, compute (a) the circulation on, and (b) the outward flux across, the boundary of the given region. Assume boundary curves are oriented counterclockwise.
$$\begin{aligned}
&\mathbf{F}=\nabla(\sqrt{x^{2}+y^{2}}) ; R \text { is the half-annulus }\\
&\{(r, \theta): 1 \leq r \leq 3,0 \leq \theta \leq \pi\}
\end{aligned}$$