Consider a spherical shell of linear magnetic material with relative permeability

placed in a uniform magnetic field

. The magnetic fields in this region can be described by a magnetic potential

. Selecting the direction of

as the axis of spherical coordinates

,

is given by

, where

is a Legendre function. The magnetic field at any point is

. The coefficients

,

in the regions with (1)

, (2)

, and (3)

are determined by considering the boundary conditions at

and

, taking into account the permeability in each region: (1) and (3)

and (2)

. As the result, the field in (1) is that of

superimposed with the contribution of a magnetic dipole. The field in (3) turns out to be uniform, with magnitude considerably lower than

. The magnetic induction or B field is obtained by

, where

or

depending on the region.