# Equation for levitation forces between the magnets and superconductor

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• kipling_01
In summary, the conversation discusses the measurement of levitation forces between magnets and a type-II superconductor, as well as the relationship between upward force and weight in levitation. The purpose of the experiment is to analyze the properties of quantum levitation and its practical applications in transportation. The speaker plans to measure the levitation forces through experiments and create a phenomenological model. However, this is a complex problem and the quality of the materials used must be verified. The conversation also mentions the need to consider factors such as flux pinning and vortex behavior in the superconductor. Ultimately, further research and empirical data are needed to fully understand and model quantum levitation.
kipling_01
TL;DR 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)?

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

kipling_01 said:
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.

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.

kipling_01 said:
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 said:
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?

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.

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.

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!

vanhees71 said:
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.

vanhees71

## 1. What is the equation for calculating levitation forces between magnets and a superconductor?

The equation for calculating levitation forces between magnets and a superconductor is known as the London equation. It is given by F = (Φ0/μ0)² x (dΛ/dz), where F is the force, Φ0 is the magnetic flux quantum, μ0 is the permeability of free space, dΛ is the change in the London penetration depth, and dz is the distance between the magnet and superconductor.

## 2. How does the distance between the magnet and superconductor affect the levitation force?

The distance between the magnet and superconductor, represented by dz in the London equation, has a direct impact on the levitation force. As the distance decreases, the force increases, and vice versa. This is because the magnetic flux between the two objects is stronger when they are closer together.

## 3. What is the significance of the magnetic flux quantum in the London equation?

The magnetic flux quantum, represented by Φ0 in the London equation, is a fundamental constant in physics that represents the smallest unit of magnetic flux. It is used in the equation to calculate the total flux passing through the superconductor, which is essential in determining the levitation force.

## 4. Can the London equation be applied to all types of superconductors?

No, the London equation is only applicable to type I superconductors. Type II superconductors have different properties and require a different equation, known as the Bean model, to calculate the levitation force between magnets and superconductors.

## 5. How accurate is the London equation in predicting levitation forces?

The London equation is a simplified model that does not take into account all factors that may affect the levitation force between magnets and superconductors. Therefore, it may not be entirely accurate in predicting levitation forces in real-world scenarios. However, it is a good approximation for simple setups and can provide a general understanding of the forces involved.

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