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This is simply a matter of force balancing. The only forces on each magnet are gravity and the magnetic repulsion from the neighbors. The top magnet must be repelled from below with a force equal in magnitude to the force of gravity on it. The next magnet down has not only its own weight pushing down, but the weight of the one above it as well. This is an ...

As lurscher mentioned in a comment, you're using the wrong units for magnetic susceptibility. $\chi$ is actually a dimensionless number that is related to the magnetic permeability of a material relative to that of a vacuum. I think you were mixing it up with the molar magnetic susceptibility, which is $\chi_\text{mol} = \mathcal{M}\chi/\rho$, where ...

Using electromagnetic flux to generate enough momentum to cause "spinning" or speeds of greater then 20 rotations per minute, can be accomplished easily using rotating fans or other objects that act as a base and move independently of the surrounding mass. but hypothetically lets say that we desire the pen to move independently of the base or the 'levitating ...