Levitation of Pyrolytic Graphite and Neodymium Magnets through the Utilization of Magnetic and Electromagnetic Fields

References: 1. http://www.trifieldmeter.com/DCMagnetometer_instructions.html 2. Nave, Carl L.. "Magnetic Properties of Solids". HyperPhysics. http://hyperphysics.phy-astr.gsu.edu/Hbase/tables/magprop.html. Retrieved on 2008-11-09. 3. http://www.hfml.ru.nl/nature-july22v400.pdf 4. http://www.dougdelamatter.com/website/science/physics/magnets04.pdf 5. Wixforth, A., Kothaus, J.P., and Weimann, G. “Quantum Oscillations in the Surface-Acoustic Wave Attenuation Caused by a Two-Dimensional Electron System”. 1986 6. Geim, A.K, and Simon, M.D.. Diamagnetic Levitation: Flying Frogs and floating magnets (invited)”. Journal of Applied Physics. 1 May 2000. 7. Souslav, A. “Resonances of piezoelectric plate embedded 2D electron system. NHMFL 8. Marsden, G. “Levitation!”. Nuts and Volts . Sept. 2003

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.

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.

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.

Experiment 3: Levitation of neodymium magnet using an electromagnet

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.

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.

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).

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.

Figure 9 Schematic diagram of circuit

Figure 11 (right) and Figure 12

(left) Levitation of a

neodymium magnet by an electromagnet

receiving a PWM signal

Figure 10 Constructed circuit

Figure 1 Levitation of a neodymium magnet between

diamagnetic plates

Figure 8 Neodymium magnet

levitated between two pyrolytic plates

(constructed kit)

Figure 7 Neodymium

magnet levitated between two

pyrolytic plates (purchased kit)

Figure 13 Construction of the

electromagnets

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.

Figure 3 Orientation of the

Neodymium magnets

Table 1 Data table of theoretical and actual data of the constructed

electromagnets

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).

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 6 Two different masses of Pyrolytic graphite levitating over 4.72mm³ Neodymium magnets

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 2 Levitating Pyrolytic graphite

plate over 12. 7 mm³ Neodymium

magnets

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 5 Levitating Pyrolytic graphite plate over N35 magnet)

Wire Size /AWG Calculated # of turns Calculated Resistance (Ω) Actual # of turns Actual Resistance (Ω) % Error of Resistance (Ω)

22  1449  14.1  1322  12.0  15 

26  568  2.2  638  2.0  9 

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).

Mounted lifting

magnets

Levitating magnet

Figure 14 Levitating magnet between two

Pyrolytic graphite plates using mounted lifting

magnets

Pyrolytic graphite plates

Notable diamagnetic materials Magnetic susceptibility (χm)

χm=Km-1 (x 10-5)

Density @ 20°C ( g/cm3 )

Ammonia  ‐0.26  0.88 

Bismuth  ‐16.6  9.78 

Mercury  ‐2.9  13.534   

Silver  ‐2.6  10.5 

Carbon (diamond)  ‐2.1  3.53 

Carbon (graphite)  ‐1.6  2.09–2.23 

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