Classical Diamagnetism and the Satellite Paradox

In typical models of classical diamagnetism (see, for example, sec. 34-4 of [1] or sec. 11.5 of [2]) the change of the magnetic moment of an “atom” is deduced when an external magnetic field increases “slowly” from 0 to B = B ẑ. The “atom” consists of an electron of charge −e and mass m that is in a circular orbit of radius r0 in the x-y plane about a “fixed nucleus” of charge e′ at the origin. It is tacitly assumed that the radius of the orbit remains r0 at all times, although this is not consistent with the effect of perturbations on motion in a 1/r potential, even if radiation is ignored (as it must be in any classical model of a stable atom). Give a model of classical diamagnetism that includes the (small) effect of changes in the radius of the orbit as external magnetic field increases. Compare the present case to the so-called satellite paradox [4, 5, 6]. The latter is that the effect of atmospheric drag on a satellite in a low orbit about the Earth is to increase the speed of the satellite as it slowly spirals inwards towards the Earth’s surface.