The Levitron® is a popular toy that provides a unique and interesting demonstration of levitation using permanent magnets. It consists of a small, spinning magnetic top and a magnetic base plate. Stable levitation is possible because of a unique coupling of the magnetic forces and torques with the gyroscopic action of the top. A simple theory of its operation, using a general axisymmetric form for the magnetic field of the base, is based on the dipole force model. With this model, the stable behavior of the spinning, levitated top may be investigated by testing various assumptions for its orientation. Stability is not possible if the top remains rigidly parallel to the axis of the base. On the other hand, if one assumes that the top remains aligned parallel to the local magnetic field during radial excursions, then stability is possible. This simple model, combined with measurements of the magnetic field along the axis, permits fairly accurate prediction of the upper and lower limits of the locus of stable equilibria.

1.
E. W. Hones and W. G. Hones, U. S. Patent No. 5,404,062 (4 April 1995).
2.
R.
Edge
,
Phys. Teach.
33
,
252
(
1995
);
R.
Edge
,
Phys. Teach.
34
,
329
(
1995
);
C. Ucke and H.-J. Schlichting, Phys. Unseren Zeit. 26, 217 (1995).
3.
http://www.edoc.com/dan/levitron.html; http://popularmechanics.com/popmech/sci/tech/U086G.html; http://www.lauralee.com/physics.htm
4.
R. Thapar, A History of India (Pelican, Aylesbury, Bucks, UK, 1982), Vol. 1, pp. 233–234.
5.
K. M. Munshi, Somanatha—The Eternal Shrine (Bharatiya Vidya Bhavan, Bombay, 1976), p. 141.
6.
J. C. Maxwell, Treatise on Electricity and Magnetism, 3rd ed. (Dover, New York, 1954), Art. 116.
7.
T. B. Jones, Electromechanics of Particles (Cambridge University Press, New York, 1995).
8.
M. V.
Berry
,
Proc. R. Soc. London, Ser. A
452
,
1207
(
1996
).
9.
M. D.
Simon
,
L. O.
Heflinger
, and
S. L.
Ridgway
,
Am. J. Phys.
65
,
286
(
1997
).
10.
R. E.
Holmes
,
J. Appl. Phys.
49
,
3102
(
1978
).
11.
T. B. Jones, J. Electrostat. 11, 85 (1981).
12.
E. Weber, Electromagnetic Theory (Dover, New York, 1965), pp. 125–127.
13.
R. M. Harrigan, U.S. Patent No. 4,382,245 (3 May 1983).
14.
C. Murakami, Proceedings of the Eighth Symposium on Electromagnetics and Dynamics (Institute of Mechanical Engineers, Tokyo, 1996), p. 461.
This content is only available via PDF.
You do not currently have access to this content.