Equation for levitation forces between the magnets and superconductor

[kipling_01]

TL;DR

How can I measure the levitation forces between the magnets and a type-II superconductor (YBCO superconductor)?

How can I measure the levitation forces between the magnets and a type-II superconductor (YBCO superconductor)?

 

[Vanadium 50]

If it's levitating, what is the relationship between upward force and the weight?

 

[ZapperZ]

Summary: How can I measure the levitation forces between the magnets and a type-II superconductor (YBCO superconductor)?

How can I measure the levitation forces between the magnets and a type-II superconductor (YBCO superconductor)?

I don't understand. Isn't the "levitation force" equal to mg, the weight of the magnet that is being levitated? If not, what exactly are you trying to find here?

Zz.

 

[kipling_01]

The purpose of my experiment is to analyze the properties of quantum levitation (or quantum locking) due to the Meissner Effect and Flux Pinning and discuss how quantum levitated vehicles such as high-speed trains could provide ways to improve the efficiency and speed of future transportations. In order for QL to be practical, I will need to levitate large masses, immediately several questions popup:

--> What is the magnitude of the levitation force?

Here I would preform several experiments where I would measure the levitation forces - above a magnet, below magnets, sideways. Afterwords, I will make an extrapolation and some calculation of what it would take to levitate actual trains/vehicles.

In summary, what I mean by levitation forces is a way to calculate the vertical forces between magnets (with different strength) and a superconductor.

 

[ZapperZ]

The purpose of my experiment is to analyze the properties of quantum levitation (or quantum locking) due to the Meissner Effect and Flux Pinning and discuss how quantum levitated vehicles such as high-speed trains could provide ways to improve the efficiency and speed of future transportations. In order for QL to be practical, I will need to levitate large masses, immediately several questions popup:

--> What is the magnitude of the levitation force?

Here I would preform several experiments where I would measure the levitation forces - above a magnet, below magnets, sideways. Afterwords, I will make an extrapolation and some calculation of what it would take to levitate actual trains/vehicles.

In summary, what I mean by levitation forces is a way to calculate the vertical forces between magnets (with different strength) and a superconductor.

This is not as trivial as you think. The force depends on the geometry of the field, and thus, the geometry of the source. It also depends on the quality of the superconductor, because one can, for example, induce flux pinning sites in the material.

You can't calculate this analytically. Anyone doing Jackson's E&M can tell you that. All you can do is make a phenomenological model based on your data.

Zz.

 

[kipling_01]

I believe that the materials I have to perform this experiment are of the highest quality. I bought it from this website: https://www.quantumlevitation.com/product/mini_maglev_kit

Through what type of measurements can I make a phenomenological model?

 

[ZapperZ]

I believe that the materials I have to perform this experiment are of the highest quality. I bought it from this website: https://www.quantumlevitation.com/product/mini_maglev_kit

Through what type of measurements can I make a phenomenological model?

This depends on what your goal is. Your state purposed:

The purpose of my experiment is to analyze the properties of quantum levitation (or quantum locking) due to the Meissner Effect and Flux Pinning and discuss how quantum levitated vehicles such as high-speed trains could provide ways to improve the efficiency and speed of future transportations.

is rather vague because you did not indicate what quantities that you wish to measure to get to that purpose. What characteristics do you wish to "analyze"? This will dictate what you will measure.

BTW, a good experimentalist never trust the quality of something without verification, especially if that something is the most crucial part of the whole experiment. Have you performed a magnetic susceptibility measurement to see how sharp the transition is, for example? Do you know if you have pinned flux or meandering flux on your sample? Have you precisely determined and verified H₁ and H₂ values?

And oh, this is not a quantum physics question anymore.

Zz.

 

[f95toli]

The quality does not really matter. Since you are cooling the superconductor in field you will create vortices and these must pin to "something" (a defect, a grain boundary etc) for the magnet to "stick" once everything is cold.
In fact, I am not even sure a perfect type II superconductor would work very well for this application; if the field from the magnet was uniform you would presumably just get an array of vortices but I don't think there would be must resistance to movement.

Hence, this is a really, really complicated problem and you would most likely need quite a bit of empirical data to even create a numerical model . Your best bet is to start looking at relevant publications; there should be quite a few papers out related to levitating trains etc.

 

[vanhees71]

Look for the Maxwell stress tensor, from which you can calculate the "magnetic pressure" on the magnet. The reason of levitation is that a superconductor is an ideal diamagnet!

 

[kipling_01]

Here is a small demonstration of how I'm going to perform my experiment: https://drive.google.com/drive/folders/1utaZYt6poPjt55r1jl74dTkQwgGbKQO5

 

[f95toli]

The reason of levitation is that a superconductor is an ideal diamagnet!

Sure, but the reason for why the magnet the magnet is stable is flux pinning and that is the complicated part.
It is possibly to levitate a magnet above a type I superconductor but it is quite hard. The reason for why it is so easy with YBCO (a type II with lots of pinning sites) is that it "freezes" the position of the magnetic field as it goes below Tc (or to be more exact the vortices form and pin in such as way the the energy is minimised for that exact field distribution); this in turn typically means that the position the magnet was in as system was cooled is very stable, if you remove the magnet and them put it back again if frequently ends up in exactly the same position.