diamagnetic levitation

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diamagnetic levitation

• dustin brumley

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what it is

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

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what is diamagnetism

• diamagnets are objects with a mag. susceptibility
  ? lt 0
• this means that diamagnetic objects repel mag.
  fields
• many things are diamagnetic like water and wood
  and frogs

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earnshaws 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

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simple proof

• easiest way to look
• at earnshaws is thru laplaces equation
• ?f0 for point charges and electrostatic
  potentials

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other ways to prove it

• you can prove earnshaws theorem by using the
  virial of the forces
• also you can prove it with gauss law but thats
  not much fun either

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now for the physics
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is there a way around earnshaws theorem to
stably levitate something?

• apparently so!

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levitation

• earnshaws 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

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whats 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

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what can we levitate?

• theoretically we can levitate anything
  diamagnetic with a given magnetic field
• this goes for walnuts, mice, leaves,
  diamondsfrogs

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atomic level
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analog to lenzs 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

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the experiment placethe university of nijmegen
HFML
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how to achieve a 16T fieldbitter magnet
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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 10C
• 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

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faqs

• can humans be levitated?
• was the frog ok?

• yes
• yes

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levitating frog
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water floats too
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acknowledgements

• mac herrera
• Berry, Geim Of Flying Frogs and Levitrons 1997
  European Journal of Physics v. 18 pp. 307-313
• Jones, W Earnshaws 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

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fin