Two parallel circular plates of radius a are located at z = 0 and z = d. The top plate (z = d) is raised to potential V₀; the bottom plate is grounded. Between the plates is a conducting material having radial-dependent conductivity, σ(ρ) = σ_0ρ, where σ₀ is a constant.

(a) Find the ρ-independent electric field strength, E, between plates.

(b) Find the current density, J between plates.

(c) Find the total current, I, in the structure.

(d) Find the resistance between plates.