Demagnetizing Factors for a Hollow Sphere

© 2010-2012 IEEE. 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 Nm decreases from 1/3 when χ > 0 and increases from 1/3 when χ < 0. In the limit a/b = 1, Nm 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.