Earnshaw (1805–1888) and Passive Magnetic Levitation

S. Earnshaw, a mathematical physicist born in England two centuries ago, was the author of studies on the transmission of sound and light. His theory on the transmission of light by “detached particles” has also influenced some studies on the stability of bodies in potential fields, particularly studies on the levitation of permanent magnets, i.e. on passive magnetic levitation. This theorem was so well known that even Maxwell mentioned it, and is today cited almost as an axiom in the ambit of passive magnetization. However, what is less well known is that the theory actually only relates to magnetostatics. In this paper, the mathematic model of the theory that refers to stability is outlined, along with some works that refer to it, in particular those on passive magnetic levitation. It is then pointed out that spaces of low instability exist in magnetostatics, and that stability may exist in the magneto-stationary and in magneto-dynamic ambit.

[1]  J. R. Hull,et al.  Attractive levitation for high-speed ground transport with large guideway clearance and alternating-gradient stabilization , 1989 .

[2]  Lewi Tonks,et al.  Note on earnshaw's theorem , 1940, Electrical Engineering.

[3]  W. T. Scott.  Who Was Earnshaw , 1959 .

[4]  N. Mclachlan.  Theory and Application of Mathieu Functions , 1965 .

[5]  Martin D. Simon,et al.  Spin stabilized magnetic levitation , 1997 .

[6]  C. Wieman,et al.  A magnetic suspension system for atoms and bar magnets , 1993 .

[7]  J. Maxwell.  A Treatise on Electricity and Magnetism , 1873, Nature.

[8]  Harry E. Burke.  Handbook of Magnetic Phenomena , 1986 .

[9]  Michael V Berry,et al.  Of flying frogs and levitrons , 1997 .

[10]  K. Uchida,et al.  High energy product Nd-Fe-B sintered magnets produced by wet compacting process , 2001 .

[11]  M. V. Berry,et al.  The LevitronTM: an adiabatic trap for spins , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[12]  James Jeans.  The mathematical theory of electricity and magnetism , 1908 .

[13]  Malcolm McCaig,et al.  Permanent magnets in theory and practice , 1977 .

[14]  William Thomson Baron Kelvin,et al.  Treatise on Natural Philosophy , 1867 .

[15]  A. Geim,et al.  Magnet levitation at your fingertips , 1999, Nature.

[16]  Edward P. Furlani,et al.  Permanent Magnet Applications , 2001 .

[17]  W. Braunbek,et al.  Freischwebende Körper im elektrischen und magnetischen Feld , 1939 .

[18]  Rev. S. Earnshaw,et al.  On the Mathematical Theory of Sound , 1860 .

[19]  H. S. Nagaraj,et al.  Investigation of Magnetic Fields and Forces Arising in Open-Circuit-Type Magnetic Bearings , 1988 .

[20]  Donald F. Wilcock,et al.  A Passive Magnetic-Thrust Bearing for Energy-Storage Flywheels , 1980 .

[21]  G. Temple.  Static and Dynamic Electricity , 1940, Nature.

[22]  R. Parker.  Advances in Permanent Magnetism , 1990 .

[23]  R. Bassani.  Permanent Magnetic Levitation and Stability , 2001 .

[24]  J. Coey,et al.  Applying Permanent Magnets , 1996 .

[25]  W. Braunbek,et al.  Freies Schweben diamagnetischer Körper im Magnetfeld , 1939 .

[26]  R. Bassani.  Stability of Permanent Magnet Bearings under Parametric Excitations , 2005 .

[27]  G. Genta,et al.  Gyroscopic Stabilization of Passive Magnetic Levitation , 1999 .

[28]  A. Geim,et al.  Detection of earth rotation with a diamagnetically levitating gyroscope , 2011 .

[29]  L. L. Helms.  Introduction to potential theory , 1971 .