Classical diamagnetism: How adiabatic change of field makes it work

Many textbooks discuss the diamagnetic response of a ``classical atom'' to a small and slowly (adiabatically) applied magnetic field. Here we show that the small-field assumption is not essential, whereas the slow rate of field change is crucial: it preserves the circular nature of the orbit regardless of the applied field magnitude. The latter property follows from the existence of an adiabatic invariant of electron's motion. Orbit circularity allows us to solve the problem for arbitrarily large fields. Resulting diamagnetic response exhibits symmetries that unexpectedly persist beyond the small-field limit, and provides a nice illustration of the range of applicability of Larmor's theorem.