by Dr. Michael V. Berry, University of Bristol
Levitating Globe is a spinning top.
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.
does it need to spin?
To prevent the top from overturning as well as provide
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.
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 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. 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
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.
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.
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.