Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Force and torque of an electromagnetically levitated metal sphere


Author: G. Lohöfer
Journal: Quart. Appl. Math. 51 (1993), 495-518
MSC: Primary 78A25
DOI: https://doi.org/10.1090/qam/1233526
MathSciNet review: MR1233526
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Abstract | References | Similar Articles | Additional Information

Abstract: The Lorentz force and torque exerted on an electrically conducting sphere exposed to an external, time-varying magnetic field are analytically calculated. The external magnetic field is generated by a set of sinusoidally alternating, but otherwise arbitrary, current density fields of different frequencies and phases. Expressions for the force and torque in a laboratory frame of reference, which is more convenient for application, are also given. Finally, the special cases of rotational and mirror-symmetric external current density fields are treated in more detail.


References [Enhancements On Off] (What's this?)

  • [1] D. M. Herlach, G. Lohöfer, R. Knauf, J. Piller, and P. Preu, Electromagnetic positioning and inductive heating under micro-g, Proceedings of the 6th European Symposium on Material Sciences under Microgravity Conditions, Bordeaux, France, December 1986, European Space Agency SP-256, 1987, pp. 437-443
  • [2] G. Lohöfer, P. Neuhaus, and I. Egry, TEMPUS--A facility for measuring thermophysical properties of undercooled liquid metals, to appear in: High Temp.-High Press. 23 (1991)
  • [3] I. Egry, B. Feuerbacher, G. Lohöfer, and P. Neuhaus, Viscosity measurement in undercooled metallic melts, Proceedings of the VIIth European Symposium on Materials and Fluid Sciences in Microgravity, Oxford, UK, September 1989, European Space Agency SP-295, 1990, pp. 257-260
  • [4] G. Lohöfer, Device for positioning and melting electrically conductive materials without a receptacle, US Patent No. 4979182, 1990
  • [5] F. R. Block and A. Theissen, Das elektromagnetische Schwebeschmelzen--ein Beitrag zu den Verfahren des tiegelfreien Schmelzens, Elektrowärme International 29, 349-354 (1971)
  • [6] W. Brisley and B. S. Thornton, Electromagnetic levitation calculations for axially symmetric systems, British J. Appl. Phys. 14, 682-686 (1963)
  • [7] E. Fromm and H. Jehn, Electromagnetic forces and power absorption in levitation melting, British J. Appl. Phys. 16, 653-663 (1965)
  • [8] P. R. Rony, The electromagnetic levitation of metals, Trans. Vacuum Met. Conference 1964 (ed. by M. A. Cocca), Amer. Vacuum Society, Boston, MA, 1965, pp. 55-135
  • [9] G. Lohöfer, Theory of an electromagnetically levitated metal sphere. I. Absorbed power, SIAM J. Appl. Math. 49 (1989), no. 2, 567–581. MR 988619, https://doi.org/10.1137/0149032
  • [10] John David Jackson, Classical electrodynamics, 2nd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1975. MR 0436782
  • [11] R. Courant and D. Hilbert, Methoden der mathematischen Physik. I, Springer-Verlag, Berlin-New York, 1968 (German). Dritte Auflage; Heidelberger Taschenbücher, Band 30. MR 0344038
  • [12] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover, New York, 1970
  • [13] George Arfken, Mathematical methods for physicists, Academic Press, New York-London, 1966. MR 0205512
  • [14] G. Lohöfer, Inequalities for Legendre functions and Gegenbauer functions, J. Approx. Theory 64 (1991), no. 2, 226–234. MR 1091472, https://doi.org/10.1016/0021-9045(91)90077-N

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DOI: https://doi.org/10.1090/qam/1233526
Article copyright: © Copyright 1993 American Mathematical Society


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