Magnetic Levitation at Room Temperature
Tai C. Chiang (first draft 8/7/2004)
|Simple and inexpensive levitation -- no batteries, no liquid nitrogen, and no complicated electronic circuits.|
Stable passive diamagnetic levitation at room temperature using permanent magnets
Many people have seen levitation tricks. A common one is a magnet floating above a piece of YBCO high-temperature superconductor cooled by liquid nitrogen. One can also levitate a frog (or other animals or objects) with a very powerful superconducting magnet. But these tricks are hard to do at home.
For levitation enthusiasts, here is a simple experiment. You can levitate a piece of graphite at room temperature using powerful permanent magnets. The cost can be as low as a dollar.
Sextupole, quadrupole, and 3x3 configurations.
Pictures for a quadrupole set.
These are some of the simplest configurations. The magnets are arranged with the north poles of adjoining magnets alternately pointing up and down. The magnets are neodymium-iron-boron (NIB) magnets coated with nickel or gold. Small ones are inexpensive. You can find many vendors on the web. You can also find such magnets in some stores. NIB magnets of 0.5-inch size or larger can be dangerously powerful and should not be used by beginners. Keep the magnets away from medical equipment, computers, monitors, TVs, cards with magnetic strips, and other magnetic objects. You can use fairly small ones for levitation. The 3x3 configuration above uses 1/8-inch cubes. High grade NIB magnets (N50 for example) are better, but the cost is higher. N38 grade is more common and cheaper, and works nearly as well.
Graphite is diamagnetic, meaning that it tends to avoid magnetic field. Many materials are slightly diamagnetic. Graphite is one of the best choices for levitation. Its diamagnetic susceptibility is small on an absolute scale, but larger than most other materials. It is also very light. The best diamagnetic material is a superconductor; it is in fact "perfect". It is very easy to levitate with superconductors, but it is not necessarily easy to find liquid nitrogen.
The alternating pole configurations shown above give rise to a strong field gradient and thus a strong levitating force. The resulting magnetic trap is stable. There are many elegant configurations. Soft iron pieces can be used to shape or enhance the field. (For the curious, you might want to do a web search on Halback array, electromagnet pole cap, maglev, and permanent magnet undulator.) Levitation is possible with just one magnet, but not with a simple cube or cylinder alone, as a dipole field does not provide a stable trap.
Shown above is an interesting configuration (you should be able to figure this out). The OD of the cylinder is 3/4-inch. It allows you to float a piece (or several pieces) of 0.5 mm pencil lead and spin it. Pencil lead contains graphite. Some brands work better than others, and smaller diameters are generally better. The 3x3 configuration also allows you to float a piece of pencil lead.
Pictures of graphite - from left to right - natural single crystals, HOPG (highly oriented pyrolytic graphite), and a piece of graphite ore.
The best result is obtained with a thin oriented graphite sheet (the diamagnetic susceptibility of graphite is anisotropic). Large graphite single crystals are great but are rare. If you know of a good source, please let me know (I use the material for experiments). HOPG is very expensive. Low grade pyrolytic graphite is inexpensive, and works just as well. Pencil lead, motor brushes, and graphite rods for industrial use are inexpensive sources of graphite, but they don't work quite as well because the graphite particles are not oriented. You can glue together pieces of 0.5 mm pencil lead to form various shapes.
2x2 (quadrupole), 3x3, and sextupole pocket demo kits.
These are great motivational tools for teachers and nice toys for older children. The rectangular magnets are 5 x 5 x 2 mm N50 magnets. The substrates (keepers) are foreign coins. 1-, 2-, and 5-cent Euro coins, made of steel coated with copper, are good choices for substrates. A substrate is not essential for levitation, but it provides a convenient assembly platform. Also, the bottom poles of the magnets can create a field canceling somewhat the levitation effect. The reduction can become significant for thinner magnets, but can be avoided by using a substrate to form a closed magnetic path. For very thin magnets, you might want to polish the coin face flat or use a commercial keeper for better magnetic coupling. Another purpose of the keeper is to suppress the field below the kit and so it can be moved freely on a steel desk. The 2x2 kit shown above, built on a Euro penny, is the best for carrying around. The field outside the box is fairly weak. To be on the safe side, keep it away from your credit cards.
3 pieces of 0.5 mm pencil lead floating above the 3x3 kit (right).
A 4x4 kit glued together. The colors indicate the poles. This assembly can self-destruct if the glue fails. Not recommended for beginners.
Challenges and suggestions for readers:
1. Design a kit that levitates something by 1 cm.
2. You might want to take a quadrupole kit with you on your next field trip and look for objects that can be levitated. If you find one, it might be a room temperature superconductor -- discovery with Nobel prize potential -- or a piece of graphite. It is not necessarily a silly suggestion. Magnesium diboride has been around for decades. Its superconducting transition at around 40 K was not discovered until 2001. If you find a room temperature superconductor, please let me know (and don't forget to cite my suggestion at your award ceremony).
3. For physics majors, here are some questions for you. What is the field strength just outside the magnet pole faces? Why are the multipole configurations stable, but not the dipole configuration? Why is graphite diamagnetic? Which elements in the periodic table are diamagnetic? What causes diamagnetism?
4. Problems for theorists: (a) calculate the susceptibility of graphite, (b) calculate the field distribution for the quadrupole configuration, and (c) calculate the height of levitation (and compare with experiment).
For an explanation of Earnshaw's theorem: M. D. Simon, L. O. Heflinger, and A. K. Geim, "Diamagnetically stabilized magnet levitation", American Journal of Physics, vol. 69, page 702 (2001).
Additional references: W. Braunbek, Z. Phys. 112, 764 (1939). R. D. Waldron, Rev. Sci. Instrum. 37, 29 (1966).