A long, cylindrical conductor of length L, radius a, and resitivity carries a steady current I

A long, cylindrical conductor of length L, radius a, and resitivity ρ carries a steady current I that is uniformly distributed over its cross-sectional area.

(a) Use Ohm's law to relate the electric field E in the conductor to I, ρ, and a.

(b) Find the magnetic field B just outside the conductor.

(c) Use the results for parts (a) and (b) to compute the Poynting vector S = E × B/μ0 at r = a (the edge of the conductor). In what direction is S?

(d) Find the flux ∫Sn dA through the surface of the conductor into the conductor, and show that the rate of energy flow into the conductor equals I2R, where R is the resistance.