Advertisement

Continuum Mechanics and Thermodynamics

, Volume 28, Issue 5, pp 1435–1444 | Cite as

The magnetic field of a permanent hollow cylindrical magnet

  • Felix A. ReichEmail author
  • Oliver Stahn
  • Wolfgang H. Müller
Original Article

Abstract

Based on the rational version of MAXWELL’s equations according to TRUESDELL and TOUPIN or KOVETZ, cf. (Kovetz in Electromagnetic theory, Oxford University Press, Oxford, 2000; Truesdell and Toupin in Handbuch der Physik, Bd. III/1, Springer, Berlin, pp 226–793; appendix, pp 794–858, 2000), we present, for stationary processes, a closed-form solution for the magnetic flux density of a hollow cylindrical magnet. Its magnetization is constant in axial direction. We consider MAXWELL’s equations in regular and singular points that are obtained by rational electrodynamics, adapted to stationary processes. The magnetic flux density is calculated analytically by means of a vector potential. We obtain a solution in terms of complete elliptic integrals. Therefore, numerical evaluation can be performed in a computationally efficient manner. The solution is written in dimensionless form and can easily be applied to cylinders of arbitrary shape. The relation between the magnetic flux density and the magnetic field is linear, and an explicit relation for the field is presented. With a slight modification the result can be used to obtain the field of a solid cylindrical magnet. The mathematical structure of the solution and, in particular, singularities are discussed.

Keywords

Magnetic field Cylindrical hollow magnet Axial magnetization Vector potential Closed-form solution Complete elliptic integrals 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Babic S.I., Akyel C.: Improvement in the analytical calculation of the magnetic field produced by permanent magnet rings. Prog. Electromagn. Res. C 5, 71–82 (2008)Google Scholar
  2. 2.
    Becker R.: Electromagnetic fields and interactions. Dover Publications, Mineola (2013)Google Scholar
  3. 3.
    Durand É.: Électrostatique. No. v. 1 in Électrostatique. Masson, Paris (1964)Google Scholar
  4. 4.
    Jackson J.D.: Classical electrodynamics. 2nd edn. Wiley, London (1975)zbMATHGoogle Scholar
  5. 5.
    Kovetz A.: Electromagnetic theory. Oxford University Press, Oxford (2000)zbMATHGoogle Scholar
  6. 6.
    Ravaud R., Lemarquand G., Lemarquand V., Depollier C.: Analytical calculation of the magnetic field created by permanent-magnet rings. IEEE Trans. Magn. 44(8), 1982–1989 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    Selvaggi J.P., Salon S.J., Chari M.V.: Employing toroidal harmonics for computing the magnetic field from axially magnetized multipole cylinders. IEEE Trans. Magn. 46(10), 3715–3723 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    Truesdell, C.A., Toupin, R.: The classical field theories. In: Handbuch der Physik, Bd. III/1, pp. 226–793; appendix, pp. 794–858. Springer, Berlin (1960). With an appendix on tensor fields by J. L. EricksenGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Felix A. Reich
    • 1
    Email author
  • Oliver Stahn
    • 1
  • Wolfgang H. Müller
    • 1
  1. 1.Fachgebiet Kontinuumsmechanik und Materialtheorie, Institut für MechanikTechnische Universität BerlinBerlinGermany

Personalised recommendations