Figure P24.82 shows a cross section through a system that consists of an infinitely long charged rod centered in a thick cylindrical shell of inner radius \(R\) and outer radius \(2 R\). The shell is made of a conducting material; the rod is made of a nonconducting material and has a uniform linear charge density. The electric field associated with the system is indicated by the field lines in the diagram. For each finite length \(\ell\) of the system, there is a charge of \(-q\) on the shell inner surface. For that same finite length \(\ell\), determine the charge on 

\((a)\) the rod and 

\((b)\) the shell outer surface.

(c) In length \(\ell\), what is the charge on the shell?

(d) What is the ratio of the surface charge density on the shell's inner surface to the surface charge density on the outer surface?

Data from Figure P24.82

cylindrical shell E charged rod 2R