Question

Radial Hall Effect 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 Er (r) is ρ(r) = ρ+ + ρc(r) where ρ+ comes from a uniform distribution of immobile

positive ions and ρc(r) = jz(r)/v comes from electrons with velocity v. Show that ρc(r) = ρc

=

−ρ+/(1 − v2/c2). Do not use special relativity.

Answer 1