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Hi! How could I calculate the amount of bismuth needed, and the magnetic field needed (of the levitated object) to levitate the magnetic material above the bismuth? (This seems easier than levitating bismuth over a magnet)
Question Date: 2008-08-12
Answer 1:

That depends on how strong your magnet is, now how big it is. The strength of magnetic field that your magnet generates is proportional to the size of the magnet, and so is its inertia. As a consequence, the more force you generate, the more force you will need. It's a question of having a well-magnetized enough substance.

I'm actually thinking at this point that some trial-and-error might be in order. At least that's what I would do. But then, I'm not a physicist, I'm a biologist, and biology is much more directly observational than physics, since there are few "laws" of biology, only common rules.

Answer 2:

I was actually incorrect in sending you that equation before.There is a better equation that would be used for diamagnetic levitation, although it's a bit trickier. I'm going to make a few simplifications to the equation, and we can take a look at what the different things mean:

B2 / z = mu_0 * p * g / x

Looking at the left hand side of the equation, B is the magnetic field we're using, and has units of Teslas; z is how thick the sample of Bismuth is in your experiment, which will have units of meters. When measuring thickness, you want to look at how thick the Bismuth is in the direction perpendicular to the magnet. This is the part of the equation that I've simplified a bit - I'll talk a bit more about that later.

Now let's look at the right hand side of the equation. As I mentioned before, mu_0 is a constant that is always the same, no matter what. The value is 1.2566 * 10-6 T m / A (Tesla meter per Amp). p is the density of whatever material we're dealing with. For Bismuth, the density is 9800 kg/m3 (kilograms per meter3). g is a constant you might have seen before - it's the acceleration on Earth due to gravity (for example, weight = m * g). Its value is 9.8 kg m/s2 (kilograms meters per second squared). Lastly, x is the susceptibility of the material we're looking at. As you mentioned before, for Bismuth, it's -1.66 * 10-4 (with no units). These numbers are just constants - the tricky stuff was on the left hand side of the equation.

So if you want to figure out how much Bismuth you need for a given magnetic field, you would plug in the value of B for whatever magnet you have, and then you can calculate z. As I mentioned, I simplified the equation a bit. Because of this, the value you get probably won't be exactly right. However, this is OK! I would suggest getting some rare-earth magnets - they're very strong, and should work well enough for what you are doing. Then, you could try calculating how thick the Bismuth should be given that, and then try an experiment to see if it works. If it doesn't, that's OK, too. Just try some different thicknesses to see what works the best.

Also, note that this equation doesn't tell us how much Bismuth we need. That's because it's actually not important how much Bismuth we have. If we have more Bismuth, it will be heavier, but it will also have a stronger magnetic field coming from it to react with the magnet. The important thing is how thick the Bismuth is.

Also, when getting a magnet, I would suggest trying to get one that has a big area. This is mostly just so that it would make it a lot easier to try to balance the Bismuth over it, although smaller ones would work well, too.

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