An electromagnetic analysis is presented for experiments with strong permanent disc magnets. The analysis is based on the well known experiment that demonstrates the effect of circulating eddy currents by dropping a strong magnet through a vertically placed metal cylinder and observing how the magnet is slowly falling through the cylinder with a constant velocity. This experiment is quite spectacular with a super strong neodymium magnet and a thick metal cylinder made of copper or aluminum. A rigorous theory for this experiment is provided based on the quasi-static approximation of the Maxwell equations, an infinitely long cylinder (no edge effects) and a homogeneous magnetization of the disc magnet. The results are useful for teachers and students in electromagnetics who wish to obtain a deeper insight into the analysis and experiments regarding this phenomenon, or with industrial applications such as the grading and calibration of strong permanent magnets or with measurements of the conductivity of various metals, etc. Several experiments and numerical computations are included to validate and to illustrate the theory.
2. Boström, A., G. Kristensson, and S. Ström, "Transformation properties of plane, spherical and cylindrical scalar and vector wave functions," Field Representations and Introduction to Scattering, V. V. Varadan, A. Lakhtakia, and V. K. Varadan (eds.), Chapter 4, 165-210, Acoustic, Electromagnetic and Elastic Wave Scattering, Elsevier Science Publishers, Amsterdam, 1991.
3. Cheng, D. K., Field and Wave Electromagnetics, Addison-Wesley, Reading, MA, USA, 1989.
4. Collin, R. E., Field Theory of Guided Waves, 2nd Ed., IEEE Press, New York, 1991.
5. Dahlquist, G. and Å Björck, Numerical Methods, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1974.
6. Fraden, J., Handbook of Modern Sensors: Physics, Designs, and Applications, 4th Ed., Springer, USA, 2010.
doi:10.1007/978-1-4419-6466-3
7. Griffiths, D. J., Introduction to Electrodynamics, 3rd Ed., Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1999.
8. Jackson, J. D., Classical Electrodynamics, 3rd Ed., John Wiley & Sons, New York, 1999.
9. Levin, Y., F. L. da Silveira, and F. B. Rizzato, "Electromagnetic braking: A simple quantitative model," Am. J. Phys., Vol. 74, No. 9, 815-817, 2006.
doi:10.1119/1.2203645
10. Levin, Y. and F. B. Rizzato, "Superconducting pipes and levitating magnets," Phys. Rev. E, Vol. 74, 066605-1-7, 2006.
11. Lide, D. R., CRC Handbook of Chemistry and Physics: A Ready-reference Book of Chemical and Physical Data. Ed. 88 (2007–2008), CRC Press, Boca Raton, Florida, 2008.
12. Nordebo, S. and A. Gustafsson, "A quasi-static electromagnetic analysis for experiments with strong permanent magnets,", arXiv:1407.0875 [physics.class-ph], 2014.
13. Olver, F. W. J., D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions, Cambridge University Press, New York, 2010.
14. Partovi, M. H. and E. J. Morris, "Electrodynamics of a magnet moving through a conducting pipe," Can. J. Phys., Vol. 84, 253-271, 2006.
doi:10.1139/p06-065
15. Saslow, W. M., "Maxwell’s theory of eddy currents in thin conducting sheets, and applications to electromagnetic shielding and MAGLEV," Am. J. Phys., Vol. 60, No. 8, 693-711, 1992.
doi:10.1119/1.17101
16. Serway, R. A., Principles of Physics, 2nd Ed., Saunders College Publication, Fort Worth, Texas, London, 1998.
17. Watson, G. N., A Treatise on the Theory of Bessel Functions, 2nd Ed., Cambridge University Press, Cambridge, UK, 1966.
18. Zemanian, A. H., Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications, McGraw-Hill, New York, 1965.
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