The Physics of Levitron
Untitled Document
The Physics of Levitron
How does the Levitron work?
Now that you have acquired your LEVITRON® and have
(Presumably mastered the art of spinning the top and placing it in its position
of stable levitation, you are perhaps beginning to feel the full sense of
wonderment that the LEVITRON® excites in many people. We receive numerous
queries from LEVITRON owners asking for an explanation of how the LEVITRON
works. Many express puzzlement that it works at all, often citing a theorem
due to Earnshaw (1,2) as proof that it should not work. Interest 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 was Dr. Michael V. Berry of the University
of Bristol. Dr. Berry, inspired by this recognition, published a thorough
exposition of the physics of the LEVITRON's operation (3). Dr. Berry's paper
is the best existing explanation of how the LEVITRON works and he kindly
prepared for us 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,
Tyndall Avenue, Bristol, BS8 1Tl, United Kingdom). William G. Hones Fascinations
Toys & Gifts, Inc.
What 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 norths) 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.
Why 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 the LEVITRON® was
discovered by Roy M. Harrigan (4).
Why 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. (between 2.5 and
3.0 inches for Fascinations' new Super LEVITRON). 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 the field from the base.
Why is the weight
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.
Why does the top eventually
fall?
The top spins stable in the range from about 20 to 35 revolutions
per second (rps). It is completely unstable 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 the LEVITRON can 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 Fascinations' new PERPETUATOR ®, an electro-magnetic pulsed device
which can keep the top levitating for many days or even weeks.
Is the LEVITRON Principle
used elsewhere?
In recent decades, microscopic particles have been studied
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 close.
References 1. S. Earnshaw, On the nature of the
molecular forces which regulate the constitution of the luminiferous ether,
Trans. Cambridge 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.
