Consider the vector field $on{R}^2$ given $by$:

$F(x,y)=(\frac{-y}{x^2+y^2},\frac{x}{x^2+y^2})$

and the circle $C$ parametrized $by$:

$$:$[0,2]R^2,(t)=(x(t),y(t))=(3cos(t),3sin(t))$

$(a)$ Compute the work integral ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*Tdsof$ the vector field $F$ along the curve $C.$

$(b)$ Compute the flux integral ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*Ndsof$ the vector field $F$ across the curve $C,$ where $N$

represent the outward pointing unit normals.

$(c)$ Briefly describe the vector field $Fon$ the circle $C(in$ particular, what $is$ its angle with the

velocities and with the normals $of$ the curve?$).$ Use this $to$ justify the result $of$ the integrals

$in(a)$ and $(b).$