I'd first like to take a moment to explain a bit about magnetic fields and all the different variables that appear, since it can be a bit confusing. What we normally think of as the magnetic field, in terms of physics, is the variable you've called B. This appears in pretty much all of the equations we use to deal with magnetic fields. To be thorough, B is actually called the magnetic induction. It has units of Teslas, or T. Another very similar quantity is the magnetic field strength, H. This is a little bit different that the magnetic induction. H is the strength of a magnetic field we'd measure in a real life experiment involving a real material. The units of H are Amperes Per Meter, or A/m. The magnetization, or M, is basically a measure of how much a material has reacted to a given magnetic field. The units of M are also in Amperes Per Meter. These quantities are all very closely related, and it can get quite confusing to remember which one is which. Be sure to understand the slight differences between the three, using the above definitions, as well the equations you listed in your question:M = susceptibility * H
B = mu_0 * (H + M)
Additionally, we've seen two more variables, the susceptibility of the material, and also mu_0. The susceptibility of a material is how strongly it will react to a given magnetic field. The greater the susceptibility, the more it will react. Additionally, as you noticed in your problem, the susceptibility can also be negative. This means that the magnetization that's generated will be opposite to the field that created the magnetization. The susceptibility you have for Bismith is correct. Also, the susceptibility of a material has no units.
Also, there's mu_0. This is a constant that's always the same - it's basically a measure of how strong the magnetic force is in the universe. Its value is 1.26 * 10-6 T*m/A (Tesla-meters per Ampere). This is called the vacuum permeability, or just the magnetic constant. Don't let the name trip you up, though - it's just a number that's always the same whenever you see it in an equation. The susceptibility, however, can and does change depending on what material we're looking at.
Getting to your problem, I'm not really sure what is supposed to be calculated or measured - the problem doesn't seem to clearly state that. You won't be able to find the size of the sample of Bismuth from any of the information given.
I'm not totally sure how you would calculate the force between the Bismuth and the magnet that is causing it to become magnetized, at least given the information you have. I believe (although I am having some trouble finding this for 100% sure) that the force between the two objects will be :F = mu_0 / 2 * M * A * H
Where A is the area of the bismuth that's facing the magnetic field. We don't know what A is, but we'll mention that in a bit.
To know whether or not this will be able to levitate the sample of Bismuth, you could find out if this force is greater than the force of gravity trying to pull the Bismuth down. If you were to do this, you would need to know the mass. However, since you notice that above we were unsure of how to find the size of the sample of Bismuth, and here we're unsure of what the mass is, we could perhaps use that to our advantage. Density is the amount of mass per unit volume (D = m / V). You could possibly use that to try to eliminate the unknown quantities of mass and area, since the density of Bismuth is something that can be looked up in a periodic table.
Hope this helps a bit to get you on track with this problem. Magnetism can be a tricky subject due to all of the weird variables. Additionally, it seems a bit cloudy on what you actually have to solve for, so it might be good to get some clarification on that, as well.
Click Here to return to the search form.