Chapter 25, Problem 75PQ

A solid sphere of radius R has a spherically symmetrical, nonuniform volume charge density given by ρ(r) = A/r, where r is the radial distance from the center of the sphere in meters, and A is a constant such that the density has dimensions M/L³.

1. a. Calculate the total charge in the sphere.
2. b. Using the answer to part (a), write an expression for the magnitude of the electric field outside the sphere—that is, for some distance r > R.
3. c. Find an expression for the magnitude of the electric field inside the sphere at position r < R.