We present an interesting connection between Brownian motion and magne
tism. We use this to determine the distribution of areas enclosed by t
he path of a particle diffusing on a sphere. In addition, we find a bo
und on the free energy of an arbitrary system of spinless bosons in a
magnetic field. The work presented here is expected to shed light on p
olymer entanglement, depolarized light scattering, and magnetic behavi
or of spinless bosons.