Chapter 17.3, Problem 69E

 55.    Rotation fields are usually not conservative

a.    Prove that the rotation field $F=\frac{\langle -y,x\rangle }{{\left|r\right|}^p}$, where r = 〈x, y〉, is not conservative for p ≠ 2.

b.    For p = 2, show that F is conservative on any region not containing the origin.

c.    Find a potential function for F when p = 2.