Von Michael V. Berry, liegt jedem Levitron Omega bei, in Englisch
Frequently Asked Questions About THE LEVITRON; by Michael V. Berry
1. 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 as a magnet with its north pole pointing up, and
the top as a magnet with its north pole pointing down. The principle is that
two similar poles (e.g., two north's) repel, and two different 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.
2. Why does it have 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. With the Levitron, the
axis is nearly vertical and the precession is visible as a shivering that gets
more pronounced as the top slows down.
3. Why doesn't the top slip sideways?
For the top to 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 precesses, deviates
slightly from vertical. 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 the field from the base.
4. 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 equik6rium 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.
5. Why are the magnets ceramic and not metal?
The magnetic field of the base pushes sideways on the electrons in the top
as they spin through the field. In a metal top, which conducts electricity,
the electrons would flow. Resistance in the metal would damp these 'eddy
currents' and dissipate the top's rotational energy, causing it to slow down
and eventually fall. The ceramic top is an insulator, so the eddy currents
6. Why does the top eventually fall?
The top spins stably in the range from about 20 to 26 revolutions per
second (rps). It is completely unstable above 30 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 (1 8 rps) and falls. The
spin lifetime of the Levitron can be extended by placing it in a vacuum. In
some vacuum experiments, the top falls after about 30 minutes. Why it does so
is not clear; perhaps the temperature changes, pushing the equilibium 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 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.
7. 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.