According to this Veritasium video, the magnetic field in a wire with a non-zero current is an artifact of special relativity. A moving charge sees a speed difference between the wire and the electrons in it (since the electrons are moving). Due to Lorentz contraction there appears to be a net positive charge and a repelling force arises. The physical speed of electrons supporting a current is very slow, a few micrometers per seconds, but due to the number of electrons and the strength of the electric field the effect is macroscopic.
What if you could mechanically increase this speed? Say you had a charged capacitor, and one of the plates was given a parallel velocity. E.g. two concentric cylinders with a charge imbalance, with one of them attached to a motor. Wouldn't that create a very strong apparent magnetic field?