External fields created by uniformly magnetized ellipsoids and spheroids

In this work we have obtained the fields for external points created by uniformly magnetized ellipsoids and spheroids. The problem is solved directly in rectangular coordinates, obtaining the potential created by a uniformly charged ellipsoid everywhere by a variational method, in contrast to the usual method due to Dirichlet. Using the preceding result, we calculate the potential created by a uniformly magnetized ellipsoid in any external and internal points, as a superposition of the potentials created by two uniformly charged ellipsoids, which have opposite charge densities and slightly shifted centers. Finally, we find the solutions for the potential and field in any point external to a uniformly magnetized spheroid in rectangular coordinates. The results are checked with the classical ones obtained in spheroidal coordinates, finding a complete agreement except in one case. A discussion of this discrepancy is given. Finally, we determine how the magnetic field behaves with distance from the ellipsoid boundaries, which is very useful for corrections of the stray field flux and search coil design and also for models of particulate recording media with uniaxial anisotropy.<>