*The same discovery was previously made in 1802 by an Italian jurist, Gian Dominico Romognosi, but was overlooked because it was published in a newspaper, Gazetta de Trentino, rather than in a scholarly journal.
1. J. Nelson, Am. Journ. Phys. 7, 10 (1939).
*Contributed by Professor Donald W. Kerst
Alternating current in a pair of magnet coils produces a magnetic field of such a shape and strength that an aluminum ball can be stably levitated.
An aluminum ball or other light, highly conducting object can be levitated by the ac magnetic field of a pair of identical coils with their axes along a vertical line and separated by a distance comparable to their diameter. When the currents in the two coils flow in opposite directions, a cusp-shaped field is produced in which the magnetic field is zero at the center point between the coils and increases in every direction outward. This magnetic well is capable of supporting stably a 10-centimeter diameter, hollow, 1-cm-thick, aluminum ball by virtue of the eddy currents induced in the ball. One can point out and demonstrate that the ball is not attracted to a permanent magnet. A hollow, 1-cm-thick, aluminum cylinder, 38 centimeters long by 8 centimeters in diameter will also levitate but at a lower equilibrium position. The cylinder executes remarkable gyrations and oscillations if set into motion. If the cylinder is cooled to liquid nitrogen temperature before being placed in the field, it will begin spinning very rapidly for reasons that are not fully understood.
If the coils are connected so that their currents flow in the same direction, a so-called magnetic mirror is formed, and a diamagnetic object like an aluminum ball has a stable position along the axis of the coils but not at right angles to the axis. Thus the ball is ejected sidewise. Because of this, it is good to hold the ball with a net bag made of a few strands of twine. The reason the ball is ejected is that the magnetic field decreases radially outward from the axis, and thus the ball rests in a magnetic well for motion along the axis, but it rests unstably at the top of a magnetic hill for motion perpendicular to the axis.
The construction of a magnetic levitation apparatus is difficult because large magnetic fields are required over a relatively small volume, and thus the coils must have a large current density and corresponding heat dissipation. For coils with a depth of about 5 centimeters in air, the cooling by free convection is sufficient for current densities of about 200 amperes per square centimeters. These coils are run at a higher current density, and dimensions as shown will allow short (30 second) periods of operation. The capacitors are chosen to resonate the coil inductance at the power line frequency (usually 60 Hertz) so that the current drawn from the power line is much less than the circulating current in the coils. The power line requires a 25 ampere capacity. The capacitance required for the mirror connection (C = 170 µF) is slightly less than for the cusp connection (C = 212 µF) because of the mutual coupling between the coils. The variac allows the ball to be well levitated when the voltmeter reads about 600 volts. The coil layers should be insulated, varnished and baked. Electric motor repair shops can do these things.
The coils and their electrical connections should be insulated to prevent electrical shock. The coils should not be overheated. One should keep one's watch and other items sensitive to strong magnetic fields out of the vicinity of the coils. Care should be taken to avoid dropping the aluminum ball, since it is rather heavy. When cooled to liquid nitrogen temperature, the ball should not be touched. When it begins to spin rapidly, it can be ejected from the region of the magnetic field with considerable force.
A permanent magnet is brought near a cathode ray tube causing a distortion of the pattern on the fluorescent screen to illustrate the effect of a magnetic field on moving charged particles.
The influence of a magnetic field on a moving charged particle can be illustrated by bringing a permanent magnet (bar or horseshoe) near the screen of a cathode ray tube. One should preface this demonstration with a discussion of the poles of a magnet and the shape of the magnetic field near the magnet. The usual demonstration with iron filings, perhaps sprinkled on a sheet of transparent plastic above the magnet and projected on a screen with an overhead projector, can be used to help the audience visualize the shape of the magnetic field. It should be pointed out that the magnetic field comes from the north pole of the magnet and loops around toward the south pole, though the direction is just a convention. One should also stress that the magnetic field lines do not terminate on the south pole of the magnet the way electric field lines do on charges but rather continue on through the iron and emerge at the north pole. Thus one cannot cut a magnet in half and isolate the north and south poles. It is not accurate to say that the field lines always close on themselves, but rather one should say that they cannot end. In practice magnetic field lines often go to infinity or wander endlessly within some bounded region of space.
Secondly, to make the demonstration effective, the audience must understand how a cathode ray tube works. One should stress the fact that the electron beam consists of a large number of negatively charged electrons moving at a good fraction of the speed of light (about 0.25c for a typical acceleration voltage of 17 kV). With a single spot on an oscilloscope screen, one can show the deflection of the spot when the magnet is brought near the screen. A horizontal line on the screen can be made to deflect upward at one end and downward at the other. The direction of the force is given by the vector qv × B which, since the charge q of the electron is negative, is in the direction of B × v, given by the right-hand rule. Alternately, working backwards, one can determine which pole of a magnet is which by noting the direction in which the beam is deflected. With a pattern such as a sine wave on the oscilloscope, many interesting shapes can be produced with the magnet. The electron beam can also be thought of as an electric current, with the current moving backwards from the screen because of the negative charge of the electrons. In this way one can introduce the idea of magnetic fields exerting forces on currents and proceed to demonstrate the usual cases of forces on currents in wires.
There are many examples of the use of magnetic fields to deflect moving charged particles. The electron beam in a television or computer monitor is deflected magnetically rather than electrically as in most oscilloscopes. Charged particle accelerators such as cyclotrons use magnets to confine the particles in a circle while they are accelerated by electric fields, and plasma confinement devices such as the tokamak use complicated magnetic fields to confine a gas of charged particles in the quest for controlled nuclear fusion. Other related examples are velocity analyzers, mass spectrometers, magnetrons, and Hall effect devices. The role of magnetic fields in astrophysics (Van Allen belts, solar wind, cosmic rays, etc.) makes an interesting digression.
It may be tempting to try this demonstration using the picture tube of a television receiver or the video monitor of a computer. Such is not advised because such tubes, especially color ones, require very precise alignment of the electron beam and contain components that can become permanently magnetized and distort the picture. Many television sets and monitors contain a special circuit that degausses the tube each time the set is turned on in an attempt to eliminate stray magnetic fields.
There are no significant hazards with this demonstration other than perhaps breaking the glass on the CRT with the magnet. If the deflection is too small, it might be tempting to remove the CRT from its cabinet in order to get the magnet closer to the beam. This is not advised since it is too easy to come into contact with the lethal high voltage used to accelerate the beam.
A large capacitor discharged into a low impedance coil of a few turns produces a magnetic field of strength sufficient to crush an aluminum soft drink can.
The soft drink can should of course be empty and have a hole in the top for the air to escape. In fact, it crushes more completely if the bottom of the can is cut away to allow the air to escape as easily as possible. A soft drink with "Crush" in its name is also preferred. A loud noise accompanies the crushing of the can, and so the audience should be warned. If the can is quickly removed, it will feel warm because of the currents induced in the can. The can is held up for the audience to see and is then passed around for closer inspection.
After crushing the can, on can ask the spectators whether they would like to see it done again. This usually elicits an enthusiastic response. This time, however, one rests the can with its bottom just touching the end of the coil, and the can is propelled out into the audience. For this demonstration, the coil axis should be aimed at about a 45° angle with respect to the vertical so that the can follows a parabolic trajectory with maximum range out into the audience. A 7-Up can with the bottom intact is preferred for this part of the demonstration. With practice one can cause the can to always land in the same seat and ask the person sitting there to try and catch it. Handing the person a baseball glove before propelling the can adds a touch of interest and clues the audience in to what is about to happen without the necessity of an explanation. In practice, the can is more often caught than not. One should be quick to apologize for aiming badly if the can is missed lest the audience boo the embarrassed victim.
The magnetic field produced by the coil is proportional to the number of ampere-turns in the coil which is given by NV(C/L)½, where N is the number of turns, V is the capacitor voltage, C is the capacitance and L is the inductance of the coil and its leads back to the capacitor. The magnetic force is proportional to the square of the field or N2V2C/L. Thus an effective demonstration requires a large voltage and capacitance and a low inductance. It appears that increasing the number of turns is advantageous, but beyond a certain point the improvement is offset by the increase in inductance with N. Alternately, one can consider that when properly designed, essentially all of the energy in the capacitor (CV2/2) is transferred to the magnetic field whose energy is approximately B2/2µo times the volume of the interior of the coil.
This demonstration illustrates a number of important physical principles. The can is crushed or propelled by virtue of the repulsive force between the current in the coil and the induced current in the can. Thus it illustrates both the force exerted on a current by a magnetic field and Faraday's law of induction. The magnetic pressure (B2/2µo) exists only in the space between the turns of the coil and the can in the brief time before the magnetic field soaks through the can. The electrical circuitry consists of a damped harmonic oscillator. The can is not attracted by a magnet, and the effect would not occur with a tin can because of its much higher electrical resistance. Cooling the can with liquid nitrogen can help to decrease its resistance, but does not provide much improvement, presumably because the can already crushes faster than the current dies away for a room-temperature, aluminum can. The necessity of letting the air escape illustrates the ideal gas law and the relation of pressure to volume and the viscosity of the air that precludes its rapid expulsion. The demonstration could be repeated with cans with different size holes for the air to escape.
The crushing of the can is analogous to the plasma theta pinch. The ripples that occur around the circumference of the can when it crushes is an example of an instability well known with plasmas, and the variation of the wavelength of the ripples could be studied in demonstrations with different types of cans. Ultrastrong magnetic fields (>107 gauss) can be produced by the clever use of explosives and used to study matter under pressure conditions found in stars and planets.
Considerable energy is stored in the capacitor, and the voltages and currents used in this demonstration are potentially lethal. The capacitor is best placed behind the lecture bench with only the coil exposed in order to protect the audience in the event of an explosion. The capacitor should not be charged above about 80% of its rated voltage. All high-voltage conductors should be well insulated. One should stand well back while it is being charged and discharged. The capacitor should be provided with a bleeder resistor or, better yet, with a shorting bar that automatically shorts the capacitor through a low resistance (<100 ohms) whenever it is not being charged or waiting to be discharged into the coil. The controls used to initiate the charge and discharge should be on a long cord and provided with a secure safety ground. The propelled can is relatively harmless unless it is aimed directly at someone. Sharp points and loose tabs should be removed from the can, however.
1. F. Bitter, Scientific American 213, 65 (Jul 1965).
A coil of wire wound around a short, cylindrical, laminated iron core is energized to propel a ring of aluminum up to the ceiling.
In an alternate version of the demonstration, a capacitor of such a value as to make the circuit resonate at near 60 Hz is placed in series with the coil. The ring can then be made to oscillate up and down on the iron core by the variation in the inductance caused by the ring's position.
The ring is propelled into the air because a current is induced in it in a direction opposite to the direction of the current in the coil. The opposing currents repel one another. The magnitude of the current induced depends upon the resistance of the ring. Thus a good electrical conductor such as aluminum or copper is required. Aluminum is preferred because of its smaller mass which enables it to accelerate more easily. The resistivity of aluminum is lowered by about a factor a seven when cooled to the temperature of liquid nitrogen. The repulsion can also be understood in terms of the tendency of the conducting ring to exclude the magnetic flux that the coil attempts to force through it. The ring is not attracted to a permanent magnet, but rather the force results from the current induced in the ring by the changing magnetic field of the coil.
The voltages required to make an impressive demonstration are potentially lethal. Even if low voltage is used to energize the coil, there is a dangerous high voltage transient across the coil when the switch is opened. Thus the coil and switch must be carefully insulated. The ring can be ejected with some force, and so the area above should be kept clear. The demonstration should not be done beneath overhead lights that could shatter. Since liquid nitrogen can cause severe frostbite, the ring should be handled with tongs during that part of the demonstration. With a little practice, one can catch the ring with the tongs to the delight of the audience.
1. C. L. Strong, Scientific American 205, 143 (Aug 1961).
High temperature superconductors are used with permanent magnets to demonstrate the Meissner effect.
What for many years was an exceedingly difficult demonstration requiring liquid helium has now become rather ordinary with the development in 1987 of materials such as yttrium-barium-copper-oxide that become superconductors at temperatures above the boiling point of liquid nitrogen (77K). These superconductivity kits are now available at low cost from a number of sources. The user need only supply liquid nitrogen which is available from hospital supply houses and other sources. At least one vendor** even markets a kit for the fabrication of superconductors requiring a kiln capable of reaching 1000°C and a medium-sized vise.
**Arbor Scientific, P.O. Box 2750, Ann Arbor, MI 48106-2750 (313) 663- 3733.
The usual demonstration consists of placing a disk of the material several centimeters in diameter in a glass dish and putting enough liquid nitrogen in the dish to just cover the disk. Then a small magnet made of a rare-earth material such as neodymium or samarium-cobalt is levitated a few millimeters above the disk. It takes about a minute for the superconductor to cool sufficiently for the effect to occur. A piece of paper or a wire hoop can be passed under the magnet to illustrate that it is really levitated. For large groups, a video camera and monitor are almost essential to allow everyone to see, although in some cases an intense point source of light can suffice to project a shadow of the magnet on a screen.
As a variation, one can start with the magnet resting on the disk before the liquid nitrogen is added. The magnet will abruptly levitate when the critical temperature is reached. If the nitrogen is allowed to boil away, the magnet suddenly falls, and whole process can be repeated. If water vapor condenses from the air, it can form a layer of ice causing the magnet to stick to the disk.
Another demonstration that can be more easily seen by a large audience requires a disk of superconductor suspended by a string about half a meter long. Beside the superconductor, one can also suspend on separate strings materials of similar size and shape but made out of plastic, iron and copper. A strong bar magnet is first brought near the plastic with no effect. Then the magnet is brought near the iron which is strongly attracted to the magnet. One then points out that plastic is an electrical insulator and iron is an electrical conductor but not as good a conductor as copper. The audience is then asked to predict the effect when the magnet is brought near the copper. If the magnet is brought slowly up to the copper, there is no effect, but if the magnet is waved back and forth next to the copper, the copper disk begins to swing. One can then explain eddy currents generated by time-varying magnetic fields.
Finally the magnet is brought up to the warm superconductor. By waving the magnet back and forth, the audience can be shown that there is no effect and the material behaves like an electrical insulator. The superconductor is then lowered into a dewar of liquid nitrogen for about a minute and the demonstration repeated. This time there is an obvious repulsion of the superconductor from the magnet. The effect persists for about a minute until the superconductor warms up again.
Another dramatic demonstration, suitable for slightly more sophisticated audiences is place a toroid of superconducting material around an iron transformer core. The transformer secondary can be connected to an incandescent lamp that ceases glowing when the superconductor is cooled. The transformer primary has to have enough series impedance to tolerate the shorted turn represented by the superconductor.
One should probably not conclude the demonstration without a comment about the potential importance of high-temperature superconductors and the difficulties of using the technology for practical applications.
A magnet will levitate above a superconductor (or a superconductor above a magnet) because of the Meissner effect which causes the magnetic flux to be expelled from a superconductor. The image one should have is of a magnet with its field lines emerging from one pole and looping around the outside to re-enter at the pole on the other end. Since these field lines cannot penetrate the superconductor, the magnet is forced to rise above the superconductor to give the field lines space to return. A superconductor is an example of a diamagnetic material, in contrast to iron which is ferromagnetic. Diamagnetic objects are drawn toward regions of weak magnetic field, whereas ferromagnetic (and paramagnetic) objects are drawn toward regions of strong magnetic field.
Liquid nitrogen or anything cooled to the temperature of liquid nitrogen should not be allowed to come in contact with any part of the body since it can cause immediate and severe frostbite. Gloves and goggles are recommended whenever liquid nitrogen is used.
1. J. Bransky, Phys. Teach. 28, 392 (1990).
2. A. M. Wolsky, R. F. Giese and E. J. Daniels, Scientific American 260, 60 (Feb 1989).
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