# Does Diamagnetism Occur Even in a Constant Magnetic Field?

• I
• hongseok
hongseok
TL;DR Summary
I learned that diamagnetism is due to Lenz's law. But doesn't Lenz's law only apply when the magnetic field changes? Why does diamagnetism occur even when a constant magnetic field is applied without change?
I learned that diamagnetism is due to Lenz's law. But doesn't Lenz's law only apply when the magnetic field changes? Why does diamagnetism occur even when a constant magnetic field is applied without change?

Lenz's depends on the flux, which changes when a current loop is rotated, so it tells you the direction in which the loop will rotate.

hongseok
hongseok
hongseok said:
TL;DR Summary: I learned that diamagnetism is due to Lenz's law. But doesn't Lenz's law only apply when the magnetic field changes? Why does diamagnetism occur even when a constant magnetic field is applied without change?

I learned that diamagnetism is due to Lenz's law. But doesn't Lenz's law only apply when the magnetic field changes? Why does diamagnetism occur even when a constant magnetic field is applied without change?
I was not in the previous thread that discussed this but I agree with the conclusion. Lenz's law has little (if any) to do with diamagnetism. Lenz's law is a dynamic property says that an EMF is created to counteract a change in magnetic flux in time. While diamagnetism is a static property, it remains even if there is no change in magnetic flux.

If you find that assertion that diamagnetism=Lenz's law in an notable physics book, please feel free to share the name of the textbook.

Mentor's note: Several posts have been split off into a new thread.

Lenz's law tells you in what direction a loop will rotate when a magnetic field is turned on.

pines-demon said:
If you find that assertion that diamagnetism=Lenz's law in an notable physics book, please feel free to share the name of the textbook.
Purcell's Electricity and Magnetism has a very interesting section that gives some insight into diamagnetism using elementary classical concepts. The section is titled "Electric Currents in Atoms" and is section 11.5 in the second and third editions, section 10.5 in the first edition. The induced electric field associated with a changing magnetic field plays a central role in the discussion. The overall change in magnetization ##\Delta m## in this classical model depends only on the overall change in the applied field ##\Delta B## and does not depend on the rate at which the applied field changes.

This classical model is not meant to be taken too seriously. To quote from the 3rd edition:

As mentioned at the beginning of this section, diamagnetism (and likewise paramagnetism and ferromagnetism) can be explained only with quantum mechanics. A purely classical theory of diamagnetism does not exist. Nevertheless, the above discussion is helpful for understanding the critical property of diamagnetism, namely that the change in the magnetic moment is directed opposite to the applied magnetic field.

TSny said:
Purcell's Electricity and Magnetism has a very interesting section that gives some insight into diamagnetism using elementary classical concepts. The section is titled "Electric Currents in Atoms" and is section 11.5 in the second and third editions, section 10.5 in the first edition. The induced electric field associated with a changing magnetic field plays a central role in the discussion. The overall change in magnetization ##\Delta m## in this classical model depends only on the overall change in the applied field ##\Delta B## and does not depend on the rate at which the applied field changes.

This classical model is not meant to be taken too seriously. To quote from the 3rd edition:

As mentioned at the beginning of this section, diamagnetism (and likewise paramagnetism and ferromagnetism) can be explained only with quantum mechanics. A purely classical theory of diamagnetism does not exist. Nevertheless, the above discussion is helpful for understanding the critical property of diamagnetism, namely that the change in the magnetic moment is directed opposite to the applied magnetic field.
I am not convinced the two phenomena (induction and diamagnetism) are importantly different. How do we then account for paramagnetism classically with current loops?

I guess a better idea would be to consider that there are permanent moments (due to some spinning charge or current loop) in the material. Paramagnetism would be some kind alignment between the moments and the field (due to magnetic torque) and diamagnetism would be closer to Larmor precession.

Disclaimer: as you said, due to Bohr-Van Leeuwen theorem, any classical analogy is doom to fail.

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