The semiclassical orbitals of a relativistic electron on a rotating sphere
threaded by an intense magnetic dipole field are examined. Several physical
ly distinct regimes emerge, depending on the relative sizes of the mass, to
tal energy, canonical azimuthal angular momentum, and magnetic field streng
th. Magnetic flux enclosed by orbits is quantized very close to the poles,
suggesting a quantum Hall-like state. Application of this system to neutron
star surfaces is outlined.