Chapter 14.7, Problem 43E

Zero curl Consider the vector field

$F=\frac{-y}{x^2+y^2}i+\frac{x}{x^2+y^2}j+zk.$

  a.    Show that ▿ × F = 0.

  b.    Show that ${\displaystyle {\oint }_{C}F\cdot dr}$ is not zero on a circle C in the xy-plane enclosing the origin.

  c.    Explain why Stokes’ Theorem does not apply in this case.