A very long solid insulating cylinder of radius a has charge distributed uniformly throughout its volume with charge density r . It is surrounded by a very long coaxial cylindrical conducting shell of inner radius b and outer radius c. The shell has no net charge.
(a) Derive expressions for the electric-field magnitude in terms of the distance r from the center for the regions r < a, a < r < b, b < r < c, r > c.
(b) Sketch the electric field lines in the regions a < r < b and r > c.
(c) Graph the electric field magnitude as a function of r.
(d) What is the surface charge density s and the linear charge density l on the inner and outer surfaces of the shell?