Surface magnetic charge densities and demagnetizing factors for rotating astroids

The cusp characteristics are investigated for a rotating astroid placed in an axially uniform magnetic field. The rotating astroid has point and line cusps. The surface magnetic charge densities are numerically calculated by the surface magnetic charge simulation method, modified for the rotating astroid. The results are illustrated for various relative permeabilities μ. The numerical results show that the charge densities concentrate with a peak in vicinity of the point cusps for μ>1 and in vicinity of the line cusps for μ<1. At the point cusps, the charge densities become zero in the cases of μ<∞ and become infinite in the case of μ=∞. To make clear the characteristics of the charge densities near the cusps, the slope factors are defined and evaluated for 0≤μ≤∞. In addition, the partial, fluxmetric, and magnetometric demagnetizing factors are evaluated by using those numerical results of the charge densities for 0≤μ≤∞. It is shown that the partial demagnetizing factor becomes negative near the point cusps for μ<∞. This reason is explained in terms of the demagnetizing field.