Let vec$(F)$ be the vector field in the figure. It is rotating counterclockwise around the $z-$axis when viewed from above. At a distance $r$ from the $z-$axis, vec$(F)$ has magnitude $2r.$ NOTE: Enter an answer in each field.

$($a$)$ Find a formula for vec$(F).$

vec$(F)=,$vec$(i)+,$vec$(j)+,$vec$(k)$

$($b$)$ Find curl vec$(F)$ using the coordinate definition and relate your answer to circulation density.

curlvec$(F)=,$vec$(i)+$

$$

vec$(j)+$

$$

vec$(k)$