Chapter 14.7, Problem 42E

Radial fields and zero circulation Consider the radial vector fields F = r/|r|^p, where p is a real number and r = 〈x, y, z〉. Let C be any circle in the xy-plane centered at the origin.

a.    Evaluate a line integral to show that the field has zero circulation on C.

b.    For what values of p does Stokes’ Theorem apply? For those values of p, use the surface integral in Stokes’ Theorem to show that the field has zero circulation on C.