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

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.

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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.

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You can use \imath and \jmath to get versions of i and j without the dots, which are nice when you want hats on them. – Zev Chonoles Apr 8 '13 at 6:35
Thanks, @ZevChonoles. – Sammy Black Apr 8 '13 at 6:36
AAA yes! thank you very much for this little trick. – user68203 Apr 8 '13 at 15:29