diamagnetic levitation

dustin brumley

what it is

• a look at diamagnetism• a look at earnshaw’s theorem• simple proof of earnshaw’s theorem• physical picture of diamagnetic levitation• experiment stuff• experimental proof

what is diamagnetism

• diamagnets are objects with a mag. susceptibility χ < 0

• this means that diamagnetic objects repel mag. fields

• many things are diamagnetic like water and wood and frogs

earnshaw’s theorem

• this theorem states that no stationary object made of charges, magnets and masses in a fixed configuration can be held in stable equilibrium by any combination of static electric, magnetic or gravitational forces

simple proof

• easiest way to look

at earnshaw’s is thru laplace’s equation

• ∆φ=0 for point charges and electrostatic potentials

other ways to prove it

• you can prove earnshaw’s theorem by using the virial of the forces

• also you can prove it with gauss’ law but that’s not much fun either

now for the physics

is there a way around earnshaw’s theorem to stably levitate

something?

apparently so!

levitation

• earnshaw’s theorem does not apply to induced magnetism

• possible for combination of gravitational and magnetic energy to have a minimum which is necessary to have stable levitation

what’s happening

• ferro and para-magnetic objects align with external fields and move toward the field maxima

• diamagnetic material align anti-parallel to external fields and move toward the field minima

what can we levitate?

• theoretically we can levitate anything diamagnetic with a given magnetic field

• this goes for walnuts, mice, leaves, diamonds…frogs

atomic level

analog to lenz’s law

the orbital motion of electrons creates tiny atomic current loops, which produce magnetic fields. when an external magnetic field is applied to a material, these current loops will tend to align in such a way as to oppose the applied field

the experiment placethe university of nijmegen HFML

how to achieve a 16T fieldbitter magnet

more about the bitter magnet

• maximum field of 20 tesla (T) (this is 400000 times the earth magnetic field) consists of two concentric electrical coils.

• the coils are powered by a 6000 kW (6MW) power supply. (20 kA, 300V)the magnet is cooled by de-ionized water of about 10°C

• the cooling water goes in axial direction through the small holes in the bitter plates of the coils, which line up exactly in every plate

faqs

• can humans be levitated?

• was the frog ok?

• yes

• yes

levitating frog

water floats too

acknowledgements

• mac herrera• Berry, Geim: Of Flying Frogs and Levitrons

1997 European Journal of Physics v. 18 pp. 307-313

• Jones, W: Earnshaw’s theorem and the stability of matter 1997 European Journal of Physics v. 1 pp. 85-88

• Simon, Geim: Diamagnetic Levitation: Flying Frogs and Floating Magnets 2000 Journal of Applied Physics v.87 #9

fin