A long, nonconducting cylinder of length and radius is placed along the axis of an infinitely long, very thin-walled conducting cylindrical shell of radius . The charge on the inner cylinder is and is uniformly distributed throughout its volume. The charge on the outer cylindrical shell is and is uniformly distributed along its length. (a) Derive an expression for the volume charge density of the inner cylinder. Express your answer in terms of , , , and physical constants, as appropriate