A floating magnet... big deal.
Ever try to do it?
I am sure at some point everyone who has ever played with a couple of magnets has tried to get one to hover in the air. I am sure they also met with amost instant failure.
If you try to use one magnet to repel the other in an attempt to make one float in mid air you soon discover that there is no way to keep the floating magnet "on top of" the field of the other magnet. Sure, you could use a stick to restrain the magnets, but somehow that is not as impressive as an untethered magnet.
If you try to use the attractive forces to make a magnet float either it doesn't get off the ground or it flies up and sticks to the lift magnet. Once again, a string could restrain it, but that isn't what we were going for.
Most people give up here, but a few of us tried ever increasingly complex arangements of magnets in an attempt to get one to float. Unfortunately, we knew nothing of Earnshaw's theorem which states that there is no possible static configuration of ferromagnets which can stably levitate an object against gravity, even when the magnetic forces are stronger than the gravitational forces. Bummer.
But, there is a loophole... diamagnetisim.
We are all familliar with ferromagnetisim, the strongest of the three magnetic properties. This is why magnets stick to steel or iron. There are two lesser known magnetic properties. Paramagnetisim and diamagnetisim.
Paramagnetisim is similar to ferromagnetisim in that paramagnetic materials are attracted to magnets but the effect is much smaller. Aluminum and oxygen for example are paramagnetic, but you need a very, very large magnet to be able to attract them like iron.
Diamagnetisim on the other hand tends to be repelled by magnets. Sort of a magnetic mirror. The effect is very weak just like paramagnetisim, but it is there. This is the loophole to Earnshaw's theorem.
The problem we have in using attraction to levitate a magnet is that the condition we want is metastable. This means that if everything is just right, it works, but if the magnets drift to close, they bang together and if they drift too far apart, they fall. it is like balancing an unsharpened pencil on end. It will stand there just fine, but one little bump or breeze and it falls over. We want a stable system where any disturbance from perfect results in forces that try to restore the system to perfect. Think of a plumb bob. If you push it away from vertical, gravity will pull it back.
If we use diamagnetisim, we can create a little pocket of stability on top of a big metastable system. If the field gradients are small, the floating magnet is strong enough, and the diamagnetic materials are carefully chosen, we can float a magnet. The idea here is that there is a diamagnetic plate above and below the region we are going to float in. We carefully adjust the lift magnet to just balance the weight of the floating magnet. The floating magnet can now hover. When it drifts too high and would be in danger of flying up to the lift magnet the upper diamagnetic plate repells the floating magnet pushing it back to the stable position. When the floating magnet drifts too low the lower diamagnetic plate repells the floating magnet pusing it back towards the stable position. If carefully aligned the floating magnet just hangs there in space.
Since the diamagnetic effects are small, but proportional to the strength of the magnetic fields, the floating magnet needs to have a very strong magnetic field, but be very light. The smaller the gradient of the lift field, the larger the region of stability. This means that the lift magnet should be very strong and quite far away. I ended up using a 10mm rare earth magnet for lift and a 2mm rare earth magnet for the floater. The diamagnetic materials are pyrolytic graphite.
A mockup was created with balsa wood, tape, and a ring stand to get the measurements worked out and to verify this would work.
Once I was happy with the mockup, I built a more presentable aparatus. The wood is from a broken pool cue and a surplus 32mm test tube keeps air currents from blowing the 2mm magnet out of the device. Three brass rods hold all the pieces together. The wooden pieces are all friction fit on to the brass rods. This lets me slide them around to get the geometry right.
Here is where I show off my diamagnetic levitation device.
Proof of concept:
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