Geomagnetic effects of the Earth's ellipticity

We analyse the external field generated by a uniform distribution of magnet ic susceptibility contained in an oblate spheroidal shell when it is magnet ized by an internal magnetic field of arbitrary complexity. The situation i s more relevant to the Earth than that of a spherical shell considered by R uncorn (1975a) tin the context of lunar magnetism), because of the larger f lattening of the Earth than that of the Moon. We find that, to first order in the susceptibility, each internal harmonic in a spheroidal harmonic expa nsion of the magnetic potential generates just one non-vanishing external f ield coefficient: unlike in the spherical case when all harmonics vanish id entically. The field generated is proportional to the susceptibility, thick ness of the shell and square of the Earth's eccentricity, and hence it appe ars that this field amplification mechanism will be very ineffective for th e Earth.