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?
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?
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.
Where can I buy a Levitron®?
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and an easy user interface.
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