Levitation of Pyrolytic Graphite and Neodymium Magnets
through the Utilization of Magnetic and Electromagnetic Fields
Introduction
Levitation is not possible using only ferromagnetic material. Therefore, our levitation research was conducted
using diamagnetic material in which a magnetic field is induced in opposition to an externally applied
magnetic field causing a repulsive force and thus making levitation possible (see Figure 1). Many materials
considered to be non-magnetic actually have diamagnetic properties and because of this, it was possible for
example to levitate a living frog in a high magnetic field as seen in the figure directly above. Also, a magnet
was able to be suspended between diamagnetic fingers (see picture in the top right) by use of a strong lifting
magnet. In our investigation, three experiments were conducted.
Conclusion:
In experiment one, several correlations were determined to exist. The size of
the magnet affected the levitating distance of the pyrolytic graphite. The larger
the magnet, the greater the distance between the magnet’s surface and the
pyrolytic graphite. The strength of the magnet also affected the levitating
distance of the pyrolytic graphite. The stronger grade of the magnet, the
greater the levitating distance. However, there was no correlation between the
thickness of the pyrolytic graphite and it’s levitating distance over the magnets.
Figure 1 Levitation of a
neodymium magnet between
diamagnetic plates
In Experiment two, the distance between the levitated Neodymium magnet and
mounted lifting magnet was able to be increased using larger lifting magnets
(figure 14).
Figure 9 Schematic diagram of circuit
Figure 10 Constructed circuit
Experiment 3: Levitation of neodymium magnet using an
electromagnet
Figure 2 Levitating
Pyrolytic graphite
plate over 12. 7 mm³
Neodymium
magnets
In experiment three, the researchers constructed an apparatus for dynamic
levitation between a permanent magnet by use of an electromagnet. The
researchers were are to levitate up to a mass of 9.45g.
Mounted
lifting
magnets
A circuit was constructed (Figure 9 schematic arrangement and Figure 10: actual circuitry) that utilized a
Hall sensor that had an output proportional to the magnetic field experienced. The closer the levitating
magnet got to the Hall sensor the stronger the signal produced. This way, the circuitry drove the
electromagnet with a Pulse Width Modulated (PWM) signal. A voltage of 14.0V and current of 0.10amp
was used. The electromagnetic had a ferrous core and so the levitated magnet would be attracted. If the
Hall sensor detected the magnet close then the PWM signal would turn the electromagnet off and the
levitated magnet would begin to fall. The Hall sensor would detect the falling magnet and a signal would
then turn the electromagnet back on and would attract the falling magnet. A stable dynamic levitation
could then be achieved (see figures 11 and 12). The levitating magnet mass was too small to levitate by
itself and mass was added to achieve dynamic equilibrium. The levitation equilibrium point has a very
narrow margin and a systematic technique of the reduction of the levitating mass by half was utilized to
achieve the electromagnetic force and gravitation force balance.
Figure 3
Orientation of the
Neodymium
magnets
Levitating
magnet
Pyrolytic graphite
plates
The data for the different size of magnets showed that the size of the magnet did affect the levitating
distance. In figure 2, the levitating plate gap is greater than the distance for the smaller 6.35mm³
magnets (figure 4) using the same sized levitating plate (both sets of magnets N52 strength). The
actual measured distance between the center of the plate and the top edge of the magnet was 1.16mm
for the 12.7 mm³ magnet and 0.649mm for the 6.35mm³ magnet.
Figure 4 Levitating
Pyrolytic graphite plate
over 6.35mm³
Neodymium magnets
Figure 11 (right)
and Figure 12
(left)
Levitation of a
neodymium
magnet by an
electromagnet
receiving a
PWM signal
Figure 5 Levitating Pyrolytic
graphite plate over N35 magnet)
Notable diamagnetic materials
Appendix A Magnetic
susceptibilities of
notable diamagnetic
materials at 20ºC
The data for the strength of the magnets showed that the levitating
distance was dependent on the strength. The N52 magnet in figure 2
had a levitating distance of 1.16mm. The N35 magnet had a
levitating distance of 0.480 mm (figure 5).
Figure 6 Two different masses of
Pyrolytic graphite levitating over
4.72mm³ Neodymium magnets
The data for the different masses of Levitating plates
was that although the gap was larger for the small
mass plate, the actual distance between the center of
plate and magnet surface was the same (Figure 6).
Two electromagnets were constructed (see figure 13) using 22 and 26 gauge copper wire. Figure 14
shows the theoretical and actual data for the electromagnets. After initial testing, the constructed
electromagnets did not provide satisfactory strength to levitate the magnet. Therefore, a purchased
electromagnet was used in the experimentation.
Figure 13
Construction of the
electromagnets
Table 1 Data table of theoretical
and actual data of the constructed
electromagnets
Experiment 2: Levitation of neodymium magnet
A kit was purchased that demonstrated the levitation of a neodymium magnet between two pyrolytic
graphite sheets using a neodymium lifting magnet mounted above them (see figure 7). Because of
size limitations with the kit, a larger apparatus was designed and constructed to increase the distance
between the suspended magnet and the levitated magnet (see figure 8). Larger magnets were added
to the constructed apparatus and the distance between the levitating magnet and mounted lifting
magnet was measured. In figure 1, the levitated magnet can be seen between the two pyrolytic
graphite plates.
Figure 7
Neodymium
magnet levitated
between two
pyrolytic plates
(purchased kit)
Figure 8
Neodymium magnet
levitated between
two pyrolytic plates
(constructed kit)
The purchased kit had a distance of 40mm between the bottom of the suspended
Neodymium magnet and the Levitating magnet (see figure 7) The constructed apparatus had
a distance of 68mm between the suspended Neodymium magnet and the Levitating magnet
(see figure 8).
Wire Size /AWG
Actual Resistance (Ω)
% Error of Resistance (Ω)
22 Calculated # of turns
1449 Calculated Resistance (Ω)
14.1 Actual # of turns
1322 12.0 15 26 568 2.2 638 2.0 9 Research was conducted to determine the ratio of the mass of the Neodymium magnet to the total
mass that was in dynamic equilibrium and the surface area of the magnet to the total levitating mass.
Two levitating masses were analyzed. One magnet was 6.35mm³ the other 8.001mm x 5.982mm x
1.486mm. The results for the total mass levitated divided by the mass of the magnet were that the
6.35mm³ had a ratio of 4.92 (total mass levitated = 9.45g) and the 8.001mm x 5.982mm x 1.486mm
had a ratio of 12.89 (total mass levitated = 6.96g). When the surface area was compared to the
levitated mass of each magnet, the results were that the 6.35mm³ had a ratio of 0.234 (surface area =
40.3225mm²) and the 8.001mm x 5.982mm x 1.486mm magnet had a ratio of 0.146 (surface area =
47.86mm²)
Figure 14 Levitating
magnet between two
Pyrolytic graphite plates
using mounted lifting
magnets
Magnetic susceptibility (χm)
χm=Km-1
(x 10-5)
Ammonia ‐0.26 Density @ 20°C ( g/cm3 )
0.88 Bismuth ‐16.6 9.78 Mercury ‐2.9 13.534 Silver ‐2.6 Carbon (diamond) ‐2.1 3.53 Carbon (graphite) ‐1.6 2.09–2.23 10.5 Lead ‐1.8 11.34 PyrolyKc Graphite ‐40.0 2.3 Sodium chloride ‐1.4 2.16 Copper ‐1 8.94 Water ‐0.91 0.9982 Acknowledgments
We would like to give thanks and recognition for our research experience . We
would like to thank Dr. Alexey Souslov who served as our mentor scientist,
James Maddox and Vaughn Williams for helping us in the design and
construction process of the apparatus in experiment 2, and Lee Marks for helping
construct the two electromagnets. Much appreciation is given to the National
Science Foundation and the National High Magnetic Field laboratory at Florida
State University for making the Research Experience Program for Teachers
possible. Special thanks goes to Dr. Pat Dixon and Jose Sanchez for supervision
in the RET process.
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