Chains of permeable spheres in an applied magnetic field

A multipole expansion is used to solve for the magnetic field of a chain of permeable spheres. The formalism allows treatment of chains involving spheres of differing radii and at arbitrary spacings along a line. The only restriction on the applied field is that it be curl-free over the volume of interest. We have examined in detail cases involving finite numbers (up to 10) of identical spheres at equal spacings in a uniform applied field. Predictions of the average magnetization of the individual spheres are in good agreement with the values obtained from pickup coil measurements on steel balls. We find that at close spacings (spheres nearly touching) accurate solutions require the inclusion of a large number of terms in the multipole expansion. In such cases, the simple dipole approximation is inadequate.