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
Full-text PDF Free Access
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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.
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
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)
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
G. Lohöfer, Device for positioning and melting electrically conductive materials without a receptacle, US Patent No. 4979182, 1990
F. R. Block and A. Theissen, Das elektromagnetische Schwebeschmelzen—ein Beitrag zu den Verfahren des tiegelfreien Schmelzens, Elektrowärme International 29, 349–354 (1971)
W. Brisley and B. S. Thornton, Electromagnetic levitation calculations for axially symmetric systems, British J. Appl. Phys. 14, 682–686 (1963)
E. Fromm and H. Jehn, Electromagnetic forces and power absorption in levitation melting, British J. Appl. Phys. 16, 653–663 (1965)
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
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M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover, New York, 1970
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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
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)
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
G. Lohöfer, Device for positioning and melting electrically conductive materials without a receptacle, US Patent No. 4979182, 1990
F. R. Block and A. Theissen, Das elektromagnetische Schwebeschmelzen—ein Beitrag zu den Verfahren des tiegelfreien Schmelzens, Elektrowärme International 29, 349–354 (1971)
W. Brisley and B. S. Thornton, Electromagnetic levitation calculations for axially symmetric systems, British J. Appl. Phys. 14, 682–686 (1963)
E. Fromm and H. Jehn, Electromagnetic forces and power absorption in levitation melting, British J. Appl. Phys. 16, 653–663 (1965)
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
G. Lohöfer, Theory of an electromagnetically levitated metal sphere: Absorbed power, SIAM J. Appl. Math. 49, 567–581 (1989)
J. D. Jackson, Classical electrodynamics, Wiley, New York, 1975
R. Courant and D. Hilbert, Methoden der mathematischen Physik, vol. 2, Springer, Berlin, 1968
M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover, New York, 1970
G. Arfken, Mathematical methods for physicists, Academic Press, New York, 1970
G. Lohöfer, Inequalities for Legendre functions and Gegenbauer functions, J. Approx. Theory 64, 226–234 (1991)
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Article copyright:
© Copyright 1993
American Mathematical Society
