Chapter 17, Problem 59P

A total charge of magnitude Q is distributed uniformly within a thick spherical shell of inner radius a and outer radius b. (a) Use Gauss's law to find the electric field within the cavity (r ≤ a). (b) Use Gauss's law to prove that the electric field outside the shell (r ≥ b) is exactly the same as if all the charge were concentrated as a point charge Q at the center of the sphere, (c) Explain why the result in part (a) for a thick shell is the same as that found in Example 17.10 for a thin shell. (Hint: A thick shell can be viewed as infinitely many thin shells.)