A particle carries a charge of \(2 q\) and is located at the origin. The particle is surrounded by a conducting shell of inner radius \(R\) and thickness \(t\). The shell carries a charge of \(-3 q\). Determine 

\((a)\) the charge on the inner surface of the shell and 

\((b)\) the charge on the outer surface of the shell.

(c) Make a qualitative plot of the electric field line density as a function of distance from the origin. Be sure to show the field line density in the hollow region, inside the material of the shell, and outside.