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Are you sure that the formula for diamagnetic force (B2/z=mu_0*p*g/x) is correct? I just want to be 100% sure so I can accurately calculate the force for the experiment, I don't want to do the experiment and find out that it was incorrect. Maybe I'm thinking this because you said you simplified it a little bit, and it seems like something is missing. If it is possible, I would like to know the unsimplifed version also, even if it is more complex. Then I could decide if it is within my knowledge to do, and I could also compare results from the simpler version of the formula. Thanks for your help, you've helped me a lot.
Answer 1:

Since that's a simplification, it's not totally correct, but I think(and hope) that it's close enough to be correct for your experiment. The full equation is this:

B * dB/dz=mu_0 * p * g / x

You can see that the only thing that changed is the left hand side, and I replaced
B2 / z with B * dB/dz. dB/dz is something from calculus.It's basically how fast B changes with respect to z. For example, if Bgoes from 5 T to 10 T in 5 meters, then dB/dz would be approximately 1T/m (Tesla per meter) over that distance. I say approximately because the magnetic field could change in a funny way, really fast at first,then slower later, so it could be different for different parts of z. But this would be the correct average value of dB/dz. And that's basically where the approximation comes in to play. In the simplified equation, I approximated dB/dz with B/z, which would roughly be the average value of dB/dz.

The simplified version should be enough if you want to find a rough value of the minimum magnetic field strength needed to levitate some Bismuth. If you were to try to compare the simplified version to the non-simplified equation, that could be tricky, because measuring dB/dzwould probably need a lot of measurements, and I think the tools to measure a magnetic field can be a bit expensive. However, it might be possible that wherever you buy your magnets from would have information on dB/dz (the rate of change of the magnetic field with respect to distance) for each magnetic. I'm not too sure about that, but it mightbe worth a shot. Good Luck!!

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