In a uniform electric field parallel to the rotation axis, the depolarization factor of an oblate spheroid Eric Weisstein's World of Math is given by
where defines an oblate spheroid in oblate spheroidal coordinates
For a sphere,
For a thin sheet,
In a uniform electric field parallel to the rotation axis, the depolarization factor of a prolate spheroid is
where defines a prolate spheroid in prolate spheroidal coordinates
For a long needle,
