Perfectly conducting cylinders with radii of 8 mm and 20 mm are coaxial. The region between the cylinders is filled with a perfect dielectric for which ∈ = 10⁻⁹/4π F/m and μ_r = 1. If E in this region is (500/ρ) cos(ωt − 4z)a_ρ V/m, find

(a) ω, with the help of Maxwell’s equations in cylindrical coordinates;

(b) H(ρ, z, t);

(c) S(ρ, z, t);

(d) The average power passing through every cross section 8 < ρ < 20 mm, 0 < ϕ < 2π.