Orbital magnetic moment versus Biot-Savart law 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.
 A: There are three certainties:
(1) The fine structure of spectral lines assigned to hydrogen atom is caused by the fine splitting of P, D, F terms in hydrogen line spectrum, (2) The fine splitting of P, D, F terms is in turn caused by an intra-atomic dipole magnetic field whose magnetic field has to have a magnitude order about one Bohr magneton, therefore a dipole magnetic field originated by an electron, and (3) This dipole magnetic field responsible for the fine structure of spectral lines assigned to hydrogen atom cannot definitely be originated by the orbital motion of the single electron in this atom, because all electrons in motion generate Biot-Savart magnetic fields, which have no magnetic moment.
Actually the key of the problem is a very simple truth: the magnetic moment of an electron cannot align to the force lines of a magnetic field generated in surrounding space by that electron itself, such a conjecture is evidently nonsensical. Therefore, the dipole magnetic field responsible for the fine splitting of P, D, F terms in hydrogen spectrum can be originated only by another electron, distinct from the radiating one, and such a second electron exist just in hydrogen molecule, not in hydrogen atom. In other words, only molecular hydrogen can have spectral lines with a fine structure, in no case atomic hydrogen.
As a matter of fact, the dissociated state of hydrogen passed through a discharge tube has always have  only one sound argument: the Stern-Gerlach experiments with hydrogen, which proved the paramagnetism of the particles in hydrogen delivered by discharge tubes, a paramagnetism assigned right from the very outset to atomic hydrogen. But a paramagnetic orthohydrogen molecule would have a ratio magnetic moment/mass similar to that of hydrogen atom, hence the same behavior in a Stern-Gerlach apparatus.
In conclusion, the fine structure of hydrogen spectral lines proves an unhappy confusion between orthohydrogen and atomic hydrogen in early physics. Moreover, the wrong assigning of hydrogen line spectrum to hydrogen atom is strengthened by many other sound arguments, from the hyperfine splitting measured for all S terms and all P, D, F fine subterms in hydrogen spectrum, to the total absence of a spectral width of hydrogen maser radiation. In the same context, now we have a probable explanation concerning the strange absence of any experimentally measured value of orthohydrogen magnetic moment.
