A line charge of infinite lenght 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
V(ρ) = k- (ρl/2*pi ε0) ln(ρ)
where k is a constant.
(a) Find k in terms of given or known parameters.
(b) Find thte electric field strength, E, for ρ > b.
(c) Find thte electric field strength, E, for ρ < b.
(d) Find the stored energy in the electric field per unit lenght in the z direction within the volume defined by ρ > a, where a < b.