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Magnet falls freely in superconducting tube

22 Sep 2006 Hamish Johnston

A magnet will encounter no electromagnetic braking force while inside a superconducting tube, predict physicists in Brazil. This is exactly the opposite of what occurs in a popular classroom demonstration involving a tube made out of a normal conductor such as copper.

Faraday’s and Lenz’s laws can be demonstrated by dropping a powerful neodynium magnet through a copper tube. The magnet takes about 25 s to fall through a two-meter-long tube — compared to less than 1 s for a non-magnetic object.

Many students are probably left wondering how the magnet would behave in a superconducting tube. Yan Levin and Felipe Rizzato at Brazil’s Federal University of Rio Grande do Sul have the answer: The magnet will fall freely as long as it is about one pipe-radius into the pipe, otherwise it does feel a force due to boundary effects ( But actually doing the experiment could be tricky because the calculations suggest that work must be done to get the magnet inside the tube in the first place.

Levin explained that the magnet induces electrical currents within the walls of the superconducting tube, which in turn create a magnetic field inside the tube. However, the symmetrical nature of the magnetic field means that it exerts no force on the magnet. This is true even when the the magnet is moving because the lack of electrical resistance in the tube means that the symmetrical magnetic field can simply follow the magnet as it falls with zero dissipation of kinetic energy.

Levin told that free fall will occur in tubes made of ideal conductors and superconductors – which have fundamentally different magnetic properties. Levin admitted that “in the case of normal type II superconductors there will be some other effects such as flux pinning of the magnetic field, which we have not taken into account in our calculations”. These effects could result in a small braking force.

Free fall appears to contradict previous calculations by the Brazilians, which suggest that the magnet should not move at all inside a pipe made of superconducting material (Am J Phys 74 815). For tubes made of conventional conductors such as copper, the braking force on a magnet is proportional to its velocity and the magnet very quickly reaches its terminal velocity inside the tube. The calculations also predict that the terminal velocity is proportional to the electrical resistivity of the pipe. Superconductors have zero resistivity, and therefore the magnet should stay put.

“The physics of the two systems are very different”, explained Levin, “As the resistivity of the metal goes down, the induced currents will no longer decay quickly and the self-induction effects can no longer be ignored — as was done in our Am J Phys paper”. Indeed, the terminal velocity should reach a minimum value as the tube crosses over from being a normal to an ideal conductor.

Levin and Rizzato have also concluded that a superconducting tube of finite length is a excellent magnetic shield, which could be exploited in the design of superconducting quantum interference devices (SQUIDs).

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