Size of a Diamagnetic for Levitation

[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?

 

[moejoe]

I got those equations from this paper:
"Diamagnetically stabilized magnet levitation" by LO Heflinger
Link: http://netti.nic.fi/~054028/images/LeviTheory.pdf

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??

 

[astrokreng]

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.