Demagnetizing Factors for a Hollow Sphere

The demagnetization problem for a hollow sphere of inner radius a, outer radius b, and material susceptibility χ is solved analytically. As a/b increases from 0 to 1, the magnetometric demagnetizing factor N
_m
decreases from 1/3 when χ > 0 and increases from 1/3 when χ <; 0. In the limit a/b = 1, N
_m
decreases from 1 to 0 as χ increases from -1 to ∞. As a/b increases from 0 to 1, the fluxmetric demagnetizing factor N
_f
decreases from 1/3 and has a negative minimum when χ <; -3/4. These features are explained conceptually and quantitatively. As an application, magnetic shielding by a spherical shell is quantitatively analyzed.