A solid conductor of circular cross section with a radius of 5 mm has a conductivity that varies with radius. The conductor is 20 m long, and there is a potential difference of 0.1 V dc between its two ends. Within the conductor, H = 10⁵ρ²a_ϕ A/m.

(a) Find σ as a function of ρ.

(b) What is the resistance between the two ends?