Demagnetizing Factors for a Hollow Sphere

Abstract

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