Ellipsoidal magnetostatic shield

The shielding factor which was applied to ellipsoidal magnetostatic shields with arbitrary orientation of axes relative to a uniform external magnetostatic field was examined. It is assumed that an ellipsoidal shell has confocal outside and inside surfaces. The corresponding Laplace field equation for the magnetic scalar potential is formulated in elliptical and rectangular coordinates, and the equation is solved by separation of variables for the appropriate boundary conditions. The solution contains Lame functions of the first and second kind. The shielding factor is expressed in terms of its ratios. The shielding factor is simplified by the introduction of the depolarization or demagnetization factor for both outer and inner ellipsoids. This expression is put in a form adaptable to special cases of spherical and spheroidal and cylindrical and other shields.