Tikalon Blog by Dev Gualtieri

Levitation

May 13, 2024

A common stage magician's illusion is levitation. As can be easily imagined, levitation of small objects, such as pens and playing cards, is done using thin threads. The threads are black, and they're rendered invisible against the magician's black clothing. More impressive is levitation of a supine person, which is accomplished by a lifting platform unseen by the audience. The magician usually passes a hoop around the person to prove levitation; but, a careful spectator will see that the hoop is passed to avoid the lever arm of the platform mechanism. In our Internet connected age, videos of these illusions are easily found online.

Heavenly body - Levitating woman on the label of Suggett & Kimball's Peerless tobacco, 1864.

(Cropped Wikimedia Commons image from the United States Library of Congress, Prints and Photographs division, digital image cph.3g04305. Click for larger image.)

Materials scientists employ actual levitation when they need to heat a metal to a temperature higher than what a crucible can withstand. I practiced levitation melting early in my career as a member of a team doing experiments on HfV₂, an alloy of hafnium with vanadium.[1-2] This alloy is a superconductor at 9.57 K, and it also absorbs hydrogen. Our objective was to see how hydrogen would affect its superconductivity.[1-2] Hafnium has a very high melting point, 2,233 °C, as does vanadium at 1500 °C. Hafnium is a very reactive metal; so, containerless melting in a vacuum was required to make the alloy.

Containerless melting was done by heating the metals in a vacuum chamber and using electrodynamic levitation in an induction coil. As shown in the figure, this coil was formed from copper tubing so that it could be water cooled to prevent its melting from radiant heat. The coil was attached to a radio frequency generator commonly used for induction heating. The currents in the coil induce eddy currents in metals contained within, and these currents heat the metals and produce a magnetic field in the metals that opposes the magnetic field of the currents in the coil to levitate the metals. When the generator is turned off, the molten alloy blob falls into a quenching bath.

A levitation coil, commonly made from water-cooled copper tubing.

The arrows show the direction of an instantaneous current.

The top coil turn is wound in an opposite direction to prevent the specimen from flying out of the coil. The conical shape concentrates the currents at the bottom to stabilize levitation, and the shape can hold the metal pieces before levitation.

A nice example of levitation heating can be seen in this YouTube video.

(Created using Inkscape.)

If you have an induction cooktop in your home, it's possible to crudely demonstrate this same electromagnetic levitation with a piece of aluminum foil. Not having an induction cooktop in my home, I haven't done this myself, but safety precautions must be observed in any experiment. In this case, the possible dangers are unknown, but there are some Internet videos demonstrating this effect. The same eddy current principle of the induction coil in the figure applies to this levitation.

As most have experienced, it's not possible to levitate a permanent magnet above another unless there's a means to prevent the top magnet from flipping over. One interesting example of unconstrained magnetic levitation is the levitation of a superconductor above a permanent magnet. The stable levitation in this case arises from the Meissner effect, the exclusion of magnetic fields from a superconductor. The permanent magnet induces eddy currents that produce a magnetic field that acts oppositely to that of the permanent magnet to cause the stable repulsion.

Eddy currents caused by oscillating magnetic fields do not appear to be responsible for the stability of some spectacular levitations by a research team from the Technical University of Denmark (DTU, Lyngby, Denmark) and the University of Modena and Reggio Emilia (Modena, Italy).[3-5] This research is a further investigation of a novel form of levitation first found by Turkish electronics engineer, Hamdi Ucar, in 2021.[5] Ucar attached one magnet with its magnetic pole-to-pole axis perpendicular to the rotation axis of a 10,000 rpm motor.[5] This magnet was able to lift a second magnet into stable levitation a few centimeters below the rotating magnet.[5] Not only that, but the second magnet could be levitated when the rotating magnet was angled to be horizontal to the Earth's gravitational field (see figure).[5]

Magnet levitated by a rotating magnet (Technical University of Denmark)

Permanent magnet levitated by a rotating magnet in a Technical University of Denmark demonstration.

In this demonstration, a common household crafting tool, a Dremel rotary tool, is used. Both magnets are high strength NdFeB magnets that are also electrically electrically conductive.

(Screenshot from an APS video. Click for larger image.)

In their detailed experiments, the research team used a rotating 19 millimeter diameter spherical NdFeB magnet to levitate floater magnets, other spherical NdFeB magnets, of 5-30 millimeter diameter.[3-5] During levitation, the floater magnets had their magnetization oriented close to the axis of rotation and toward the like pole of the rotor magnet, contrary to the expectation that the magnetization should be perpendicular to the magnetization of the rotor magnet.[3-4] Levitation of smaller floater magnets was more difficult, requiring a higher rotational speed to achieve levitation at a greater separation.[3-4] In all cases, levitation ceased after a time, unless an aluminium plate was placed below the floater magnet to dampen its oscillation by eddy currents.[3-4] In that case, perpetual levitation was achieved.[3-4]

It was determined that the induced eddy currents inside the magnets are extremely small; so, the eddy current mechanism can't be responsible for the levitation.[5] It's proposed that the stable levitation arises from magnetostatic forces caused by a small tilt in the relative rotational axes of the magnets.[5] This magnetostatic cause for the magnetic levitation does not require gravity as a balancing force.[3-4] Numerical simulations found that the rotating magnetic field causes a torque on the floater magnet, and the floater magnet and rotating magnet experience both attractive and repulsive forces that balance in the levitation.[5]

Levitation

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