An infinitely long straight wire of negligible cross-sectional area is at rest and has a uniform linear charge density q0 in the inertial frame K′. The frame K′ (and the wire) move with a velocity v parallel to the direction of the wire with respect to the laboratory frame K.
(a) Write down the electric and magnetic fields in cylindrical coordinates in the rest frame of the wire. Using the Lorentz transformation properties of the fields, find the components of the electric and magnetic fields in the laboratory.
(b) What are the charge and current densities associated with the wire in its rest frame? In the laboratory?
(c) From the laboratory charge and current densities, calculate directly the electric and magnetic fields in the laboratory. Compare with the results of part a.