A coaxial transmission line has inner and outer conductor radii a and b. Between conductors (a < ρ < b) lies a conductive medium whose conductivity is σ(ρ) = σ₀/ρ, where σ₀ is a constant. The inner conductor is charged to potential V₀, and the outer conductor is grounded.

(a) Assuming dc radial current I per unit length in z, determine the radial current density field J in A/m².

(b) Determine the electric field intensity E in terms of I and other parameters, given or known.

(c) By taking an appropriate line integral of E as found in part (b), find an expression that relates V₀ to I.

(d) Find an expression for the conductance of the line per unit length, G.