Moving point charge

Magnetic field at point P for a point charge ‘+q’ moving with velocity is

In any arbitrary volume of conductor net negative & positive charge is equal, thus net charge enclosed for any section is zero, hence electric field outside a current carrying conductor is zero. Also if an observer moves along the free electrons of a current carrying conductor with a velocity equal to drift velocity of free electrons, then the magnetic field experienced at the observer location will be due to relative velocity of positive ions of conductor w.r.t. observer.