 Solution

An ideal current-carrying wire consists of opposite charge populations, one associated with the stationary lattice and one with drifting carriers. They may cancel in the lattice frame while carrying a net current, as in part (c), up to exchanging the charge signs and current direction. In a carrier-rest description their densities no longer cancel because the two populations undergo different length contractions. The wire then has both electric fields and magnetic fields.

A neutral steady current in one frame generally becomes a charged steady current in another. This illustrates how electric fields and magnetic fields are parts of one relativistic field rather than separately invariant forces. Real resistive wires also have a driving longitudinal electric field and geometry-dependent surface charges; the infinite uniform filament model isolates the transverse fields of a neutral current and does not describe every field of a complete circuit.