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Hi! Thanks for the answers. To answer your question (What is the density of bismuth?) The density of bismuth is about 9.80 g/cm3. Is that how I can figure out the answers to some of the questions I asked? (How do I calculate the size of the sample of bismuth, etc..?) I NEED TO KNOW HOW TO DO THAT! Also, when I am able to figure that out, about how strong of a magnet do you think I will need to propel, or levitate, the bismuth?

Also, because you said that the magnetization of bismuth is measured in Teslas, then how do I calculate the force (Newtons) on the bismuth from those calculations? I NEED TO KNOW HOW TO DO THAT! Thanks again for that information.
Question Date: 2008-08-11
Answer 1:

I am afraid that I do not know exactly what a Tesla is. According to Wikipedia, it's 1 N/(A*m), or alternatively 1 kg/(C*s). Magnetic field is measured in Teslas. Magnetic susceptibility is measured in A/m. Naively, if you multiply the units of magnetic field with the units of magnetic susceptibility, the units you are left over with is N/(m2), which are the units of a pressure. I would guess, therefore, that the magnetic force or diamagnetic force would be equal to the magnetic field (in teslas) times the magnetic susceptibility (in amperes per meter) times the area of what is being magnetized (in square meters), which would give you units of Newtons, thus being the units of force. After that it's just F = ma as I'm sure you understand. Now that you have the density of bismuth, you can also get the mass, since mass is just density times volume. You will have to convert from cgs units to mks units, of course. What I cannot explain is whether there are some other constants that you need to multiply in; there is a 4*pi goes in there somewhere, and I would guess that this is where. More importantly, I don't know what the area is exactly; I would guess that it is the area of the diamagnet facing the magnet that it is interacting with, since this would determine the magnetic flux of the situation. I will note that 4*pi*r2 is the surface area of a sphere, which may be why the 4*pi is in there, and that would also indicate that area would be the entire surface area of the diamagnet, not just the cross-sectional area that faces the magnet. Lastly, this is from Wikipedia, which is usually pretty accurate, but not always!

If you have any further questions, I cannot keep track of what all of the symbols are (i.e. B, H, M) and what their units are. I would feel much more confident about my answer if I did; if you have any further questions, including the definitions of each of those symbols would help me to help you. Nonetheless, my GUESS is the following; see if it meshes up to the equations you have:

Force = magnetic field * magnetic susceptibility * surface area of the diamagnet
Acceleration necessary to levitate against one Earth gravity = 9.81 m/(s2) = force / (density * volume)
I hope that helps!

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