# Discuss Bill Compton's answer to: Dependence of an induced magnetic dipole on the field that induces it.

Can you show mathematically that diamagnetism alone exerts a repulsive force. Thus, diamagnetism can produce levitation. Note that a magnetic field induces a magnetic dipole with an opposite field to ...

Your question can be divided into three parts which we shall discuss separately.  However, the mathematical rationale is a bit complex, which your illustration fails to demonstrate.

The nature of diamagnetism.  Note that the magnetic field is applied in one magnet and induced in another showing the same polarity, hence we have repulsion.  We need to bring both into a superconductive state for the action to be significant: see the Meissner Effect.

The Lorentz Effect is wholly different from the Meissner Effect in that the Lorentz Effect operates at ninety degrees from the applied force and is sequential, hence we suffer specific related inefficiency of the Meissner Effect.

The Bose Effect is a paramagnetic vector that operates between the Lorentz Effect and Meissner Effect, rendering yet further inefficiency.

(Courtesy Wikipedia):

Theory of diamagnetism

The Bohr–van Leeuwen theorem proves that there cannot be any diamagnetism or paramagnetism in a purely classical system. Yet the classical theory for Langevin diamagnetism gives the same prediction as the quantum theory.[11] The classical theory is given below.

Langevin diamagnetism

The Langevin theory of diamagnetism applies to materials containing atoms with closed shells (see dielectrics). A field with intensity B, applied to an electron with charge e and mass m, gives rise to Larmor precession with frequency ? = eB / 2m. The number of revolutions per unit time is ? / 2?, so the current for an atom with Z electrons is (in SI units)[11]

The magnetic moment of a current loop is equal to the current times the area of the loop. Suppose the field is aligned with the z axis. The average loop area can be given as , where is the mean square distance of the electrons perpendicular to the z axis. The magnetic moment is therefore

If the distribution of charge is spherically symmetric, we can suppose that the distribution of x,y,z coordinates are independent and identically distributed. Then , where is the mean square distance of the electrons from the nucleus. Therefore . If is the number of atoms per unit volume, the diamagnetic susceptibility is

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