Chapter 14.4, Problem 61E

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

a.    Verify that the divergence of F is zero, which suggests that the double integral in the flux form of Green’s Theorem is zero.

b.    Use a line integral to verify that the outward flux across the unit circle of the vector field is 2π.

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