3B Scientific Diamagnetic Levitation Apparatus User Manual

3B SCIENTIFIC3B SCIENTIFIC

3B SCIENTIFIC®

3B SCIENTIFIC3B SCIENTIFIC

U45051 Diamagnetic Levitation Apparatus

Instruction Sheet

1/04 ALF

PHYSICSPHYSICS

PHYSICS

PHYSICSPHYSICS

®

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The Diamagnetic Levitation Apparatus allows the dem­onstration of the mode of action of diamagnetic ma­terials.

1. Safety instructions

• Keep all the magnets away from electronic equip-

ment, magnetic media and delicate instruments.

• The ring magnets are brittle and may break if

dropped.

• The graphite plate are easily broken or scratched.

Handle with care.

• The cube shaped magnet is very brittle and may

break merely by flying to the ring magnets.

• Use only finger pressure to tighten the hex nuts.

• If needed clean only with mild dish soap. Do not

use abrasive cleaners or solvents.

2. Description, technical data

Within a plastic bell housing there are two graphite
plates. Between these plates a cubic shaped NdFeB­magnet, plated with 24K gold, levitates freely. The gravi­tational force acting on the magnet is almost entirely
counteracted by the force of attraction from a ring
magnet located above the plastic covering. The two
diamagnetic graphite plates, one above and one be­low the NdFeB magnet, compel it into a stable equi­librium since both poles of the magnet are repelled by
the graphite plates (diamagnetism).

Dimensions:
Base plate: 95 mm x 95 mm
Height: 135 mm

1 Base plate
2 Plastic bell housing
3 Plastic plate
4 Graphite plate
5 NdFeB-magnet
6 Retaining ring
7 Hex nut
8 Ring magnets

2.1 Scope of delivery

1 Levitation apparatus
2 Transparent plastic plates
1 Socket wrench

3. Theory

The physicist S. Earnshaw proposed the following theo­rem in 1848: it is not possible for charges or magnets
to be placed in a stable levitated state in a static field
obeying an inverse square law. He further stated, how­ever, that it would be possible to achieve this with the
help of diamagnetic materials.
The availability of very powerful rare-earth metal mag­nets has made it possible to design a levitation appa­ratus such as this using graphite as the diamagnets.
Diamagnetic materials are repelled from both magnetic
poles.
The action of this levitation apparatus may be under­stood in terms of either forces, or potential energy.
The force of earth's gravity pulls downward on the cube
magnet, while the ring magnets exert an upward force.
The position of the ring magnets is chosen in such a
way, that the two forces equal each other. If the gravity
is stronger than the force of attraction, the cubic mag­net will fall down. In the opposite case it will move
upwards.
The diamagnetic property of graphite effects the cubic
magnet in such a way that it is repelled from the re­spective plate. This force is tiny but it is enough to sta­bilize the NdFeB-magnet in a state of stable equilib­rium.
To get a deeper understanding of the state of equilib­rium we look at the potential energy of the cubic mag-

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net. The graph in figure 1 shows the potential energy
of the cube if it were located at different heights within
the apparatus, assuming the ring magnets and graph­ite plates were removed. Masses tend to move to the
place where their potential energy is the lowest. To
move them to a higher place where their potential
energy is greater one has to do work and expend en­ergy.

Potential energy

Bottom Position in bell housing Top

Fig.1: Potential energy of the cubic magnet at different positions in

the apparatus without graphite plates and without ring mag­nets

Potential energy

Bottom Position in bell housing Top

Fig. 3:Total potential energy of the cubic magnet at different posi-

tions in the apparatus with plastic plates

Potential energy

The next graph in fig. 2 considers the potential energy
of the cube as the result only of the nearness to the
ring magnets, assuming that gravity is not a significant
force. Its potential energy would be the lowest at a
position closest to the ring magnets. We would have to
expend energy to remove it from the magnets and it
would gain this energy as potential energy.

Potential energy

Bottom Position in bell housing Top

Fig.2:Potential energy of the cubic magnet at different positions in

the apparatus without graphite plates and no gravity

The third graph in fig. 3 shows the total potential en­ergy of the cubic magnet in various positions within
the apparatus, when both the gravity and the attrac­tion of the ring magnets are considered. Of special in­terest is the area between the vertical lines, which rep­resent the positions of the plastic plates. Fig. 4 shows
this area magnified.

Bottom Position in bell housing Top

Fig.4: Magnification of fig.3

The graph shows that the cube has the greatest poten­tial energy at a point approximately half way between
the plastic plates. At this point the cube magnet is in
equilibrium, but it is unstable equilibrium.
If the plastic plates are now replaced by the graphite
plates, we would have to expend energy to push the
cube magnet closer to the graphite plates. Its poten­tial energy would be greater near the graphite plates.
The graph in fig. 5 shows this fact.

Potenzielle Energie

Position des NdFeB-Magneten

Grafitplatte Grafitplatte

Fig.5: Potential energy of the cubic magnet between the graphite plates

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