Chapter 6, Problem 84AP

A total charge Q is distributed uniformly throughout a spherical volume that is centered at $o_1$ and has a radius R. Without disturbing the charge remaining charge is removed from the spherical volume that is centered at $o_2$ (see below). Show that the electric field everywhere in the empty region is given by

   $\stackrel{\to }{E}=\frac{Q\stackrel{\to }{r}}{4\pi {\epsilon }_0{R}^3}$

where $\stackrel{\to }{r}$ is the displacement vector directed from $o_1$ to $o_2$ .