How the Levitron¨ Works
does the LEVITRON® work? Many people express
puzzlement that it works at all. Those who have studied in the physical
sciences often cite a theorem due to Earnshaw1,2 as
proof that it
in the LEVITRON® has
always run high among scientists. Recently, analogies of the LEVITRON® to
traps for microscopic particles (e.g., electrons, neutrons) have
been recognized by scientists working in the fascinating
area of research where matter is manipulated and examined, one such
microscopic particle at a time. The first to recognize the analogy
Dr. Michael V. Berry of the University of Bristol. Dr. Berry, inspired
by this recognition, published a thorough exposition of the physics
of the operation of the LEVITRON®3.
Dr. Berry's paper is the best existing explanation of how the LEVITRON® works
and he kindly prepared a brief encapsulation of its major themes,
which we present below. Those
wishing to read the full exposition should request a copy of the paper
from Dr. Berry (c/o the H. H.. Wills Physics Laboratory, Royal Fort,
Avenue, Bristol, BS8 1Tl, United Kingdom).
Frequently Asked Questions
About Levitron® Physics
Michael V. Berry
holds the top up? The 'antigravity' force that repels the top from
the base is magnetism. Both the top and the heavy slab inside the base
box are magnetized, but oppositely. Think of the base magnet with its
north pole pointing up, and the top as a magnet with its north pole
pointing down (fig 1). The principle is that two similar poles (e.g.,
two north poles) repel and that two similar poles attract, with forces that
are stronger when the poles are closer. There are four magnetic forces
on the top: on its north pole, repulsion from the base's north and attraction
from the base's south, and on its south pole, attraction from the base's
north and repulsion from the base's south. Because of the way the forces
depend on distance, the north-north repulsion dominates, and the top
is magnetically repelled. It hangs where this upward repulsion balances
the downward force of gravity, that is, at the point of equilibrium
where the total force is zero.
does it need to spin? To prevent the top from overturning. As well
as providing a force on the top as a whole, the magnetic field of the
base gives a torque tending to turn its axis of spin. If the top were
not spinning, this magnetic torque would turn it over. Then its south
pole would point down and the force from the base would be attractive
- that is, in the same direction as gravity - and the top would fall.
When the top is spinning, the torque acts gyroscopically and the axis
does not overturn but rotates about the (nearly vertical) direction
of the magnetic field. This rotation is called precession (fig 2).
With the LEVITRON®,
the axis is nearly vertical and the precession is visible as a shivering
that gets more pronounces as the top slows down. The
effectiveness of spin in stabilizing a magnetically supported top such
as that the LEVITRON® was
discovered by Roy M. Harrigan4.
doesn't the top slip sideways? For the top it remain suspended,
equilibrium alone is not enough. The equilibrium must also be stable
, so that a slight horizontal or vertical displacement produces a force
pushing the top back toward the equilibrium point. For the LEVITRON®,
stability is difficult to achieve. It depends on the fact that as the
top moves sideways, away from the axis of the base magnet, the magnetic
field of the base, about which the top's axis precessed, deviates slightly
from the vertical (fig. 2). If the top precessed about the exact vertical,
the physics of magnetic fields would make the equilibrium unstable.
Because the field is so close to vertical, the equilibrium is stable
only in a small range of heights - between about 1.25 inches and 1.75
inches above the center of the base. The Earnshaw theorem is not violated
by the behavior of the LEVITRON®.
That theorem states that no static arrangements of magnetic (or electric)
charges can be stable, alone
or under gravity. It does not apply to the LEVITRON® because
the magnet (in the top) is spinning and so responds dynamically to
is the weight so critical, and why must it be adjusted so often?
The weight of the top and the strength of magnetization of the base
and the top determine the equilibrium height where magnetism balances
gravity. This height must lie in the stable range. Slight changes of
temperature alter the magnetization of the base and the top. (as the
temperature increases, the directions of the atomic magnets randomize
and the field weakens). Unless the weight is adjusted to compensate,
the equilibrium will move outside the stable range and the top will
fall. Because the stable range is so small, this adjustment is delicate
- the lightest washer is only about 0.3% of the weight of the top.
does the top eventually fall? The top spins stable in the range
from about 20 to 35 revolutions per second (rps). It is completely
above 35-40 rps and below 18 rps. After the top is spun and levitated,
it slows down because of air resistance. After a few minutes it reaches
the lower stability limit (18 rps) and falls. The spin lifetime of
be extended by placing it in a vacuum. In a few vacuum experiments
that have been done the top fell after about 30 minutes.
Why it does so is not clear; perhaps the temperature changes, pushing
the equilibrium out of the stable range; perhaps there is some tiny
residual long-term instability because the top is not spinning fast
enough; or perhaps vibrations of the vacuum equipment jog the field
and gradually drive the precession axis away from the field direction.
Levitation can be greatly prolonged by blowing air against an appropriately
serrated air collar placed around the top's periphery so as to maintain
the spin frequency in the stable range. Recently a LEVITRON® top
was kept rotating for several days in this way. But the most successful
means to prolong the top's levitation is with the new Levitron PERPETUATOR®,
an electro-magnetic pulsed device which can keep the top levitating
for many days or even weeks.
the LEVITRON® Principle
used elsewhere? In recent decades, microscopic
particles have been studies by trapping them with magnetic and/or electric
fields. There are several sorts of traps. For example, neutrons can
be held in a magnetic field generated by a system of coils. Neutrons
are spinning magnetic particles, so the analogy of such a neutron trap
with the LEVITRON® is
1 S. Earnshaw, On the nature of the molecular forces which
regulate the constitution of the luminiferous ether,
Phil. Soc. 7, 97-112, 1842.
2 L. Page and N.I. Adams, Jr., Principles of Electricity,
3rd edition p. 24, D. Van Nostrand Co., New York, 1958.
3 M. V. Berry, The LEVITRON® and
adiabatic trap for spins, Proc. Roy Soc. Lond., A (1996) 452, 1207-1220.
4 R. M. Harrigan, Levitation device, U.S. Patent $,382245,
May 3, 1983.