How Are the Meissner Effect and Lenz's Law Related?

[Jiachao]

Hi, really quick question.

Is there a relationship between the Meissner effect (in superconductors) and Lenz's law.

Also, can the Meissner effect alone explain why a magnet can levitate over a superconductor, or do I need to learn about flux trapping (which isn't required by my syllabus).

 

[f95toli]

Hi, really quick question.

Is there a relationship between the Meissner effect (in superconductors) and Lenz's law.

I can't think of any "helpful" connection. The Meissner effect is ultimately a microscopic effect so you need QM for a full explanation (e.g. calculate the penetration depth).

Also, can the Meissner effect alone explain why a magnet can levitate over a superconductor, or do I need to learn about flux trapping (which isn't required by my syllabus).

The Meissner effect explains why the field is repelled so in that respect it explains the levitation. But it does not explain why a magnet can find a stable configuration (and does not "fall off") when levitated over a type II superconductor; for that you need to know something about flux trapping.

 

[Bob S]

Many years ago, I measured the ac inductance (imaginary part of impedance) of the Fermilab Tevatron superconducting dipole magnets, as the magnets cooled from liquid nitrogen to liquid helium temperature (4.2 kelvin), and back. I used a 1 amp signal, with frequencies ranging from 10 Hz to 5 KHz. At about 9 or 10 kelvin, the inductance abruptly dropped from 49 mH to 45 mH at all frequencies, the difference being due to the ac magnetic field being excluded from the volume occupied by the superconducting coils (Meissner Effect). See attached jpg. The dropoff in inductance at higher frequencies is due to ac losses in laminated iron collars, cryostats, etc. The real part of the magnet impedance was simultaneously measured, and showed no change.

 

[0xDEADBEEF]

[...]
Is there a relationship between the Meissner effect (in superconductors) and Lenz's law.

I do think that there is something of Lenz' law going on. If the superconductor would enhance the field instead of weakening it, then we would have a build up of magnetism between two Superconductors. Creating field energy out of nothing until the superconductivity breaks down. But otherwise the Meissner effect is not the same as normal induction.

Also, can the Meissner effect alone explain why a magnet can levitate over a superconductor, or do I need to learn about flux trapping (which isn't required by my syllabus).

Diamagnetism is all it needs, there are other things floating in magnetic fields if the field strength is high enough. So yes the Meissner effect is enough.

On the other hand the hanging superconductors that fly need flux trapping.