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Recently [EPL, 86, (2009) 17001], we had simulated the classical Langevindynamics of a charged particle on the surface of a sphere in the presence of anexternally applied magnetic field, and found a finite value for the orbitaldiamagnetic moment in the long-time limit. This result is surprising in that itseems to violate the classic Bohr-van Leeuwen Theorem on the absence ofclassical diamagnetism. It was indeed questioned by some workers [EPL, 89,(2010) 37001] who verified that the Fokker-Planck (FP) equation derived fromour Langevin equation, was satisfied by the classical canonical density in thesteady state, obtained by setting d/dt=0 in the FP equation. Inasmuch as thecanonical density does not contain the magnetic field, they concluded that thediamagnetic moment must be zero. The purpose of this note is to show that thisargument and the conclusion are invalid -- instead of setting d/dt=0 one mustfirst obtain the fundamental time-dependent solution for the FP equation, andthen calculate the expectation value of the diamagnetic moment, and finallyconsider its long-time limit (i.e., $t \to \infty$). This would indeedcorrespond to our numerical simulation of the dynamics. That this is indeed sois shown by considering the simpler analytically solvable problem, namely thatfor an unbounded plane for which the above procedure can be carried outexactly. We then find that the limiting value for the expectation of thediamagnetic moment is indeed non-zero, and yet the steady-state FP equationobtained by setting d/dt=0 is satisfied by the canonical density. Admittedly,the exact analytical solution for the sphere is not available. But, the exactsolution obtained for the case of the unbounded 2D-plane illustrates our pointall right. We also present some further new results for other finite butunbounded surfaces such the ellipsoids of revolution.

A note on the possibility of classical orbital diamagnetism for an unbounded system --the Bohr-van Leeuwen Theorem