  We consider the electron gas moving on the surface of a sphere in a uniform
magnetic field. An exact solution of the problem is found in terms of oblate
spheroidal functions, depending on the parameter $p= \Phi/\Phi_0$, the number
of flux quanta piercing the sphere. The regimes of weak and strong fields are
discussed, the Green's functions are found for both limiting cases in the
closed form. In the weak fields the magnetic susceptibility reveals a set of
jumps at half-integer $p$. The strong field regime is characterized by the
formation of Landau levels and localization of the electron states near the
poles of the sphere defined by a direction of the field. The effects of
coherence within the sphere are lost when its radius exceeds the mean-free
path.
