|
How the LEVITRON® Works
William G. Hones - Fascinations
Toys & Gifts, Inc.
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 credited 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 operation of the LEVITRON® (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).
Some Frequently Asked Questions About LEVITRON® Physics
Dr. Michael V. Berry
|
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 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.
|
|
|
|
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 that 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 LEVITRON® Tops). 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 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.
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 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 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.
|