How the Levitron¨ Works
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 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 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 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.