Consider a charge distribution (r) in rigid, uniform motion with velocity . (a) Show that the magnetic field produced by this system is B(r) =

Consider a charge distribution ρ(r) in rigid, uniform motion with velocity υ.
(a) Show that the magnetic field produced by this system is B(r) = (ν/c²) × E, where E(r) is the electric field produced by ρ(r) at rest.
(b) Use this result to find B(r) for an infinite line of current and an infinite sheet of current (both uniform) from the corresponding electrostatic problem.