An infinitely long cylindrical conductor carries a constant current with density jz(r).
(a) Despite Ohm’s law, compute the radial electric field Er (r) that ensures that the radial component of the Lorentz force is zero for every current-carrying electron.
(b) The source of E_r (r) is ρ(r) = ρ₊ + ρ_c(r) where ρ+ comes from a uniform distribution of immobile positive ions and ρ_c(r) = j_z(r)/ν comes from electrons with velocity v. Show that ρc(r) = ρc =−ρ₊/(1 − ν²/c²). Do not use special relativity.
(c) Estimate the potential difference from the center to the surface of a copper wire with circular cross section 1 cm2 that carries a current of 1 A.