Consider a spherically symmetric configuration: A spherical charge distribution has radius R_A and *nonuniform* charge density rho(r) = rho_zero R_A / r. It is encircled by a conducting shell with inner radius R_B and outer radius R_C (R_A < R_B < R_C). Therefore, there are four regions:
I. charged ball: 0 < r < R_A
II. gap (air) R_A < r < R_B
III. conductor R_B < r < R_C
IV. outside (air) r > R_C
a) Find the electric field in all four regions as a function of radius (E_I(r), E_II(r), E_III(r), and E_IV(r))
b) Find the electric potential in all four regions as a function of radius (V_IV(r), etc.) Take V=0 at infinite radius.
Note : R_A means R subscript A etc.
This is a good example of application of Gauss' law to determine the electric field and potential in different regions.