Chapter 14.4, Problem 60E

What’s wrong? Consider the rotation field $F=\frac{\left(-y,x\right)}{x^2+y^2}$.

a.    Verify that the two-dimensional curl of F is zero, which suggests that the double integral in the circulation form of Green’s Theorem is zero.

b.    Use a line integral to verify that the circulation on the unit circle of the vector field is 2π.

c.    Explain why the results of parts (a) and (b) do not agree.