How to find $\operatorname{div} F$ and $\operatorname{curl} F$ of the vector field $F=\hat r=\cos\theta \hat{\imath} + \sin\theta \hat{\jmath}$

Question

I was given a bunch of divergence and curl questions in class but I am stumped on this one. If anyone can help explain what I should do with it I would appreciate it.

Calculate $\operatorname{div} F$ and $\operatorname{curl} F$ of the vector field $F=\hat r=\cos\theta \hat{\imath} + \sin\theta \hat{\jmath}$.

I understood div and curl for Cartesian coordinates but I don't know what to do here. Again, any help is appreciated.

Answer 1

In cartesian coordinates, $$ \vec{F} = \frac{x}{\sqrt{x^2 + y^2}} \hat{\imath} + \frac{y}{\sqrt{x^2 + y^2}} \hat{\jmath}. $$

You can probably calculate $\operatorname{div} \vec{F}$ and $\operatorname{curl} \vec{F}$ now.