Magnetostatic self and interaction energies can be computed via demagnetization factors whenever the magnetic state is close to a uniform state, e.g. in the presence of a strong applied field, or when the dimensions involved are within the single-domain limit. We derive analytical expressions for the demagnetization factors of cylindrical shells and rings with rectangular and square cross-sections. The factors are given either as a combination of elliptic integrals or as a series expansion in powers of the dimensionless ratio between inner and outer radii. Limiting cases are analysed for particular ranges of the shape parameters. We also investigate the ring with a square cross-section, and the elliptic ring, where analytical expressions are provided only for small eccentricity. Finally, we introduce the dipolar coupling integral encoding magnetostatic interactions between a magnetized cylinder and a thin coating on its lateral surface.
- Demagnetization factor
- Magnetostatic energy
- Dipolar interaction
- Shape anisotropy
Beleggia, M., Vokoun, D., & De Graef, M. (2009). Demagnetization factors for cylindrical shells and related shapes. Journal of Magnetism and Magnetic Materials, 321(9), 1306-1315. https://doi.org/10.1016/j.jmmm.2008.11.046