That magnetic fields circulate around current-carrying wires is an empirical fact. This fact was described by the Biot Savart law. It is consistent with the other laws of electromagnetism as described the Maxwell’s equations.

The magnetic field is now understood to be part of the relativistic electromagnetic field. In the laboratory reference frame, a current-carrying wire has equal quantities of positive and negative changes. The negatively-charged electrons drift along the conductor at a very slow speed. The positively-charged nuclei effectively remain at rest. The absolute values linear charge densities of positive charges and negative charges are equal. Thus, current-carrying wires are electrically neutral. [A linear charge density is charge per unit length: λ=dqdx.λ=dqdx.]

In the reference frame of the electrons, however, things are different. The total number of positive and negative charges remain equal. The linear charge density of electrons is essentially the same as observed in the laboratory. However, the positive background of nuclei is moving with respect to the electrons. The separation between positive charges is length-contracted which increases the linear density of the positive charges.

The upshot is that in the reference frame of conduction electrons, any given length of the conductor has a net positive charge. This net positive charge produces an electric field in the reference frame of conduction electrons. In the laboratory reference frame, this electric field is seen as a magnetic field.

#aashkam
#ankit anand