I wasn't quite sure how to do the second part of this question:(adsbygoogle = window.adsbygoogle || []).push({});

Given [tex]\textbf{f}(x,y,z) = (y/(x^2+y^2), -x/(x^2+y^2), 0)[/tex] where [tex](x,y) \neq (0,0)[/tex], verify that [tex]\nabla \times f = 0[/tex].

(A) Find a scalar field [tex]\phi[/tex] such that [tex]\textbf{f} = \nabla \phi[/tex] on [tex]R_1 = \{(x,y,z): y > 0\}[/tex].

(B) Show that there does NOT exist [tex]\psi[/tex] such that [tex]\textbf{f} = \nabla\psi[/tex] on [tex]R_2 = \{(x,y,z): (x,y) \neq (0,0)[/tex]

For (A), I found [tex]\phi = [/tex] arctan(x) + arccot(x) - arctan(y/x).

I'm not sure how to do (B). In fact, I'm not even sure why it's true.

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# Potential functions

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