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# Forces on a small diamagnetic sphere in an AC/DC field

- To: femm@yahoogroups.com
- Subject: Forces on a small diamagnetic sphere in an AC/DC field
- From: "nortonsm" <nortonsm@yahoo.com>
- Date: Tue, 01 Oct 2002 07:00:06 -0000
- User-agent: eGroups-EW/0.82

    I'm trying to work out the forces experienced by a very small
    diamagnetic metallic sphere in a nonuniform magnetic field. In one
    case the magnetic field is DC, in the other AC. Now what I do know
    (which might not be much!):

    1) the small (micron size range) particle should have complete field
    penetration at the frequencies of interest

    2) A static magnetic non-uniform field (like that above a current
    ring) will suspend a diamagnetic particle (Diagmagnetic Suspension:
    "Magnetic Fields" Knoepfel, H.E.John Wiley and Sons, 2000)

    3) An AC field will induce oscillating currents in the particle. Due
    to its small size and moderate frequencies, the quasistatic limit
    should hold. These induced "eddy currents" will generate an induced
    magnetic field which should change the forces on the suspended
    particle.

    My question: I'm more interested in the AC case since as referenced
    above, the DC case is covered in Knoepfel's book. What will be the
    result in terms of forces of an AC magnetic field on the suspension
    of the particle? How do I go about doing this calculation?
    Basically,what I don't know is what limitations or "simplifications"
    I can do when dealing with VERY small metal diamagnetic particles?
    Are the induced eddy currents significant at all in particles with
    such small size?

    I'm currently demo'ing Femlab to model this problem. This problem
    obviously has azimuthal symmetry if one imagines a diamagnetic
    sphere hovering above the center of a coil. I understand how to
    model the coil, but Im not sure how to specify the boundary
    conditions on the diamagnetic sphere (say its made of silver). Some
    choices I have on boundary conditions include:
    1) Electric insulation/continuity: n(dot)J=0, n(curl)H=0
    or
    2) Magnetic discontinuity: n(curl)H1=n(curl)H2

    Any thoughts or references would be appreciated. Thanks!!!

    -Scott

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