Using the results of Problem 75, we can find the electric field at any radius for any spherically symmetrical charge distribution. A solid sphere of charge of radius R has a total charge of q uniformly
spread throughout the sphere. 

(a) Find the magnitude of the electric field for r ≥ R. 

(b) Find the magnitude of the electric field for r ≤ R.
(c) Sketch a graph of E(r) for 0 ≤ r ≤ 3R.

Data From Problem 75

(a) Use Gauss’s law to prove that the electric field outside any spherically symmetrical charge distribution is the same as if all of the charge were concentrated into a point charge. 

(b) Now use Gauss’s law to prove that the electric field inside a spherically symmetrical charge distribution is zero if none of the charge is at a distance from the center less than that of the point where we determine the field.