Chapter 17.6, Problem 60E

Radial fields and spheres Consider the radial field $F=r/{\left|r\right|}^p$, where r = 〈x, y, z〉 and p is a real number. Let S be the sphere of radius a centered at the origin. Show that the outward flux of F across the sphere is $4\pi /a^{p-3}$. It is instructive to do the calculation using both an explicit and parametric description of the sphere.