Surface Coil Winding Profile for Obtaining a Uniform Magnetic Field inside a Spheroidal Body

Uniform magnetic field generation is one of the key issues in many physical applications; such as magnetic resonance imaging, magnetic probs etc. There are many ways to obtain highly homogeneous fields. For instance, ellipsoidal bodies - and in special, spheroids - naturally maintain uniform magnetic field inside their bodies, without any need for shimming. Thanks to their rotational symmetry in addition, spheroids are easier to produce and handle, and therefore deserve more emphasis. However, creating a uniform magnetic field inside a spheroid is only possible via maintaining certain current profiles on its surface. In this paper we have derived exact surface coil winding profiles for both prolate and oblate spheroids by reorganizing state of the art derivations in the literature and correcting them whenever necessary.