A line charge of infinite length lies along the z axis and carries a uniform linear charge...

A line charge of infinite length lies along the z axis and carries a uniform linear charge density of ρℓ C/m. A perfectly conducting cylindrical shell, whose axis is the z axis, surrounds the line charge. The cylinder (of radius b), is at ground potential. Under these conditions, the potential function inside the cylinder (ρ < b) is given by

where k is a constant. (a) Find k in terms of given or known parameters. (b) Find the electric field strength, E, for ρ < b. (c) Find the electric field strength, E, for ρ > b.(d) Find the stored energy in the electric field per unit length in the z direction within the volume defined by ρ > a, where a < b.