Demagnetization factors for cylindrical shells and related shapes

Marco Beleggia, D. Vokoun, M. De Graef

Research output: Contribution to journalJournal articleResearchpeer-review


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.
Original languageEnglish
JournalJournal of Magnetism and Magnetic Materials
Issue number9
Pages (from-to)1306-1315
Number of pages10
Publication statusPublished - 2009
Externally publishedYes


  • Demagnetization factor
  • Magnetostatic energy
  • Nano-ring
  • Core-shell
  • Dipolar interaction
  • Shape anisotropy


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