# Size of a Diamagnetic for Levitation

• moejoe
In summary, the conversation revolves around the problem of diamagnetic levitation using pyrolitic graphite and rare Earth magnets. The research paper being discussed highlights the importance of the vertical stability of the levitating magnet, which is achieved when a specific equation is satisfied. This equation depends on the susceptibility and spacing between the diamagnetic slabs, rather than their dimensions. The conversation also mentions the possibility of using a single particle of this material, but it is not sufficient for levitation. The paper referenced is "Diamagnetically stabilized magnet levitation" by LO Heflinger, which discusses the theoretical aspects of this phenomenon. The conversation also speculates about the potential energy involved in the levitation process.
moejoe
Hello,

I have been interested in the problem of diamagnetic levitation where you have typically 2 slabs of some pyrolitic graphite (which is diamagnetic) and between it you have some rare Earth magnet that's levitating thanks to those graphites (and 1 more magnet somewhere above).
I have been looking into a research paper that states that the vertical stability of the floating magnet is achieved when:
$$K_v = C_z - \frac{1}{2} M B'' > 0$$
where $$C_z = \frac{6 M^2 |\chi| \mu_o}{\pi D^5}$$
M: Magnetic Dipole Moment
B'': double derivative of the magnetic field B
X: Magnetic Susceptibility
mu: Permeability of free space
D: gap between the 2 diamagnetic slabs

It's interesting to note that it does not depend on the dimensions of the diamagnetic slabs at all, rather only on the susceptibility of them and the spacing between them.
So I get the impressions that a single particle of this stuff will suffice... which it obviously doesn't. When there's no slab the Cz term is 0, when there's only one of them its divided by 2. Anyone have any knowledge about this?

I got those equations from this paper:
"Diamagnetically stabilized magnet levitation" by LO Heflinger

I was thinking it may have to do with some kind of potential energy of the diamagnetic with relation to the levitating magnet, so for example a big magnet vs. small diamagnetic might not work out too well.. i don't know.. does anyone know??

Hello,

Thank you for bringing this research to my attention. The equation you have mentioned is indeed a key factor in understanding diamagnetic levitation. As you correctly pointed out, the size of the diamagnetic slabs does not affect the stability of the levitating magnet. This is because the force of diamagnetism is a property of the material itself, not its size. In other words, a larger slab of pyrolitic graphite will not generate a stronger diamagnetic force compared to a smaller slab.

However, the spacing between the slabs and the strength of the magnet do play a crucial role in achieving stable levitation. The equation you have mentioned is a representation of the balance between the magnetic force and the restoring force of the diamagnetic material. When this balance is achieved, the magnet will remain suspended in mid-air.

To answer your question about using a single particle of diamagnetic material for levitation, it is possible to achieve this with a very strong magnet and precise control of the spacing between the particle and the magnet. However, in practical applications, using multiple slabs provides a more stable and controllable levitation setup.

I hope this helps clarify the concept of diamagnetic levitation. Further research and experimentation in this area can lead to exciting developments in fields such as transportation and energy storage. Thank you for your interest in this topic.

## 1. What is a diamagnetic material?

A diamagnetic material is a substance that exhibits a weak repulsive force when placed in a magnetic field. This is due to the alignment of the material's electron orbits in the opposite direction of the applied magnetic field, causing a repulsion between the two.

## 2. How does diamagnetism relate to levitation?

Diamagnetic materials can be levitated in strong magnetic fields due to their repulsive force. When placed in a strong enough magnetic field, the repulsive force can overcome the weight of the material, causing it to float or levitate in the air.

## 3. What is the size limit for a diamagnetic material to levitate in a magnetic field?

The size limit for a diamagnetic material to levitate depends on the strength of the magnetic field and the weight of the material. Generally, smaller diamagnetic materials are easier to levitate, but with a strong enough magnetic field, larger materials can also be levitated.

## 4. Can all materials be diamagnetic and levitate?

No, not all materials are diamagnetic. Only certain materials, such as bismuth, graphite, and water, exhibit strong enough diamagnetic properties to levitate in a magnetic field. Other materials, such as iron and nickel, are paramagnetic and are attracted to magnetic fields.

## 5. What are some potential applications of diamagnetic levitation?

Diamagnetic levitation has potential applications in transportation, such as high-speed trains that use magnetic levitation to eliminate friction. It can also be used in material handling and in medical research, where levitation can be used to study the effects of gravity on biological processes.

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