Two conducting spherical shells are arranged concentrically. The outer shell bears a total charge of +3Q; the (smaller) inner shell has a total charge of -Q. Assume that the charges are distributed uniformly over the surfaces.
(a) Draw a diagram for this situation and sketch the electric field lines in the nearby space.
(b) Use Gauss's law to find the magnitude of the electric field in all three regions: i) inside both spheres ii) between the spheres and iii) outside both spheres. Express E as a function of the distance r from the common center.
(c) Find the total charges that reside on the inner and outer surfaces of both spheres. Briefly explain your reasoning for each answer.
(d) Based on your answer in (c), sketch a picture to show both charge distributions on each shell and electric field lines created by the charges.