MOTION MOUNTAIN

214 5 electromagnetic effects
F I G U R E 158 Trapping a metal sphere using a variable speed drill
and a plastic saddle.
Challenge 209 ny
Ref. 178
Ref. 172
Ref. 170
F I G U R E 159 Floating ‘magic’ nowadays available in toy shops, left, with a spinning top and, right, with
a spinning magnetic sphere levitating above a large ring magnet (© Kay Kublenz).
levitation, until they decay.
Diamagnets levitate if∇B 2 >2μ 0 ρg/χ, whereρis the mass density of the object and
χ=1−μ/μ 0 its magnetic susceptibility. Sinceχis typically about10 −5 andρof order
1000 kg/m 3 , field gradients of about1000 T 2 /m are needed. In other words, levitation
requires fields changes of10 T over10 cm, which is nowadays common for high field
laboratory magnets.
Recently, scientists have levitated pieces of wood and of plastic, strawberries, water
droplets, liquid helium droplets as large as2 cm, grasshoppers, fish and frogs (all alive
and without any harm) using magnetic levitation. Indeed, animals, like humans, are all
made of diamagnetic material. Humans themselves have not yet been levitated, but the
feat, expected to require40 T and large amounts of electrical power, is being planned
and worked on. In fact, a similar feat has already been achieved: diamagnetic levitation
is being explored for the levitation of passenger trains, especially in Japan, though with
little commercial success.
Time-dependent electrical or magnetic fields, e.g. periodic fields, can lead to levitation
in many different ways without any consumption of energy. This is one of the methods
used in the magnetic bearings of turbomolecular vacuum pumps. Also single charged
particles, such as ions and electrons, are now regularly levitated with Paul traps and Pen-
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net