Classical electromagnetic theory uses axial pseudo-vectors to describe magnetic interactions. It is impossible to explain adequately magnetic interaction at the micro level (elements of conductors and the magnetic interactions of charges) by axial vectors. As a result, the correct form of interactions in classical electrodynamics is only an integral one. The differential formulas for magnetic interactions violate the third Newton’s law.
In the paper, we use polar vectors (real physical vectors) to describe magnetic interactions. On this way, we show that the real physical magnetic field, in contrast to the solenoidal field of the axial vector magnetic induction B, has two components: a potential field with nonvanishing divergence and a solenoidal field with vanishing divergence. These two fields act separately and independently and have different models of interactions.
Doing so, we can write differential form for the Ampere’s law obtaining correct formula for the magnetic interactions and adequate interpretation of the Biot-Savart law.
Chaplygin ball over a fixed sphere: an explicit integration
