Are you sure that the formula for diamagnetic
force (B^{2}/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 /
xYou can see that the only thing that
changed is the left hand side, and I replaced
B^{2} / 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 nonsimplified 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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