Is diamagnetism really related to lenz's law?

Question

I've visited multiple resources and read a lot of questions here on the nature of diamagnetism. I still don't understand if it truly has anything to do with lenz's law. In Walter Lewin's electromagnetism lectures, he says that this is wrong. It has nothing to do with lenz's law and cannot be understood without quantum mechanics. This is because the applied field is permanent so there's no change in field strength or flux, at least after the field has gone from zero to maximum. This makes sense, but it still doesn't explain the phenomenon. Some books, like Notling's Quantum theory of magnetism and Feynman's lectures do say that lenz's law does have something to do with it. Multiple answers here too say the same thing. Yet Nolting's book affirms that there can be no classical theory that fully explains magnetism. Isn't Lenz's law a classical rule? An answer here to a previous question of mine does say that thinking of electrons as orbiting the nucleus in circular orbits is very outdated and strictly not true. I agree, but still don't understand. So my questions are

1. If the field is indeed permanent, how does lenz's law operate here?
2. If we have a single electron in a single atom, not a molecule, the same effect should happen. The applied field, if it is changing, should induce currents that produce fields opposite to the direction of the applied field. This would make the magnetization negative. How, then, do we observe paramagnetism?
3. I've read in griffith's electrodynamics and also in Feynman's lectures that the field changes the speed of electrons, hence changing the orbital angular momentum and orbital magnetic moment such that the change in magnetic moment is opposite in direction to the field. Magnetic forces do no work, but a changing magnetic field induces an electric field which exerts forces on the electrons. But this, again, assumes a changing field. This does not need to be the case. So how are these effects explained in the case of a permanent field?

Answer 1

1. No, there are different phenomena. Possibly your confusion comes from the fact that there are diamagnetic insulators like wood and also diamagnetic conductors like copper. In the first case in a changing magnetic field there are no Eddy currents formed where the Lenz law applies and would oppose to the external magnetic field change and in the second case Lenz effect is present.

Diamagnetism is a different phenomenon where a steady external magnetic field is presented to a diamagnetic material. There are no Eddy currents. Diamagnetic dominant materials will be in this case always repelled by the external magnetic field independent polarity of the external field applied (which is not the case for the Lenz effect which can be both attractive or repulsive):

Above, the induced magnetic moments inside a diamagnetic dominant material always oppose an external magnetic field (see large arrow, illustrating the magnetic moment direction of an external applied field South to North magnetic polarity). However, this effect with the exceptions of bismuth and pyrolitic carbon, is very weak and in most cases not observable. A very large external magnetic field must be applied in order to have a visible effect in most of the diamagnetic materials. Usually we refer to these materials as non-magnetic. In reality, all macroscopic materials are magnetic in the sense that they all react but in different ways to magnetism. There is no such thing like a "magnetic neutral" material. Superconductors although exhibit a behavior similar to very strong diamagnetism are a different phenomenon.

2. Paramagnetic dominant materials have all of their magnetic domain moments aligned to an external magnetic field moment and therefore are always attracted by an external magnetic field. However they usually have much less magnetic permeability than ferromagnetic materials and therefore are weakly magnetized. You can have a paramagnetic conductor like Aluminum or a paramagnetic insulator like oxygen O2. Paramagnetism, diamagnetism, ferromagnetism etc. are collective condensed matter phenomena and you cannot apply these to the single electron.

3. Too many sub-questions which are manly irrelevant to your main question. If you are referring specifically how diamagnetism (i.e. magnetic behavior of material under a steady applied external magnetic field) works inside a material at the collective atomic scale level?

Then here is a quote from WP:

"Specifically, an external magnetic field alters the orbital velocity of electrons around their nuclei, thus changing the magnetic dipole moment in the direction opposing the external field. Diamagnets are materials with a magnetic permeability less than μ0 (a relative permeability less than 1)."

I believe your source of confusion is because you are equalizing the meaning of the word "velocity" from the above quote with the meaning of speed. You can have a steady speed but in the same time a change in velocity meaning a change in the direction of motion. Velocity is a vector, speed is not a vector but a scalar value.

Therefore, change of velocity refers here not in the change of orbital speed but in the change of orbital direction thus for example from CW to CCW. This would flip the spin angular momentum vector of the electron and therefore also its magnetic moment direction.