A rectangular conducting plate lies in the xy plane, occupying the region 0 < x < a, 0 < y < b. An identical conducting plate is positioned directly above and parallel to the first, at z = d. The region between plates is filled with material having conductivity σ(x) = σ₀e^−x/a, where σ₀ is a constant. Voltage V₀ is applied to the plate at z = d; the plate at z = 0 is at zero potential. Find, in terms of the given parameters,

(a) The electric field intensity E within the material;

(b) The total current flowing between plates;

(c) The resistance of the material.