A spherical shell has inner radius R_in and outer radius R_out. The shell contains total charge Q, uniformly distributed. The interior of the shell is empty of charge and matter.
a. Find the electric field strength outside the shell, r ≥ R_out.
b. Find the electric field strength in the interior of the shell, r ≤ R_in.
c. Find the electric field strength within the shell, R_in ≤ r ≤ R_out.
d. Show that your solutions match at both the inner and outer boundaries.