Magnetic Flux, Angular Momentum, and Statistics

It is demonstrated that the orbital angular momentum $l_z$ of a particle of charge $q$ orbiting around a tube with magnetic flux $\Phi$ is quantized in units $l_z=\mathrm{integer}-\frac{q\Phi }{2\pi }$. A very simple physical argument for this is presented, and applied to understand the Dirac quantization condition and the charge-spin relation for particles bound to magnetic monopoles. The unusual statistics of flux-tube-charged-particle composites is discussed.