In atomic physics, the fine structure of spectral lines assigned to atomic hydrogen has always been explained by considering an orbital magnetic moment of atomic electron. Still this concept is inconsistent with the basic laws of electromagnetism.
Consider a circular electric current of radius $r$, whose constant intensity is $I = nev/2πr$, where $n$ is the number of conduction electrons, $e$ is their elementary electric charge, and $v$ is their constant linear velocity. This circular electric current originates in surrounding space a dipole magnetic field measured by a magnetic moment $M = IS$, where $S = 4πr^2$. As all magnetic fields are generated by elementary electric charges in motion, this dipole magnetic field is evidently the vector sum of all magnetic fields originated simultaneously by all conduction electrons in the considered circular current. Conforming to Biot-Savart law reduced to the peculiar case of a single electron, the force lines of magnetic field generated by an electron in motion are at every moment concentric circles placed in planes perpendicular to its momentary linear velocity vector. Obviously, such a Biot-Savart magnetic field cannot be defined by a magnetic moment.
Now consider a single electron in uniformly circular motion on the same trajectory of radius $r$. Formally, we can assimilate this electron to a circular electric current with constant intensity $I = ev/2πr$, but evidently this single electron cannot originate a dipole magnetic field measured by a magnetic moment. The shape of all subsequent Biot-Savart magnetic field generated moment by moment by this single electron remains the same all the time, but their orientation in space changes every moment concurrently with the change of motion direction of the electron. And these subsequent Biot-Savart magnetic fields are not cumulative in time. It is very clear, a single electron in motion on a closed plane trajectory definitely cannot originate a dipole magnetic field defined by a magnetic moment. Therefore, the Biot-Savart law proves the falsity of the orbital magnetic moment invented for justifying the fine structure of spectral lines assigned to atomic hydrogen.
However, the fine splitting of these spectral lines is a reality experimentally noticed, so that the dipole magnetic field with magnetic moment about one Bohr magneton has to be found as responsible for this spectral splitting effect.
What is the only possible solution of this apparently unsolvable issue? Please use your logic to answer.