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

- To: femm@yahoogroups.com
- Subject: Re: Forces on a small diamagnetic sphere in an AC/DC field
- From: "nortonsm" <nortonsm@yahoo.com>
- Date: Wed, 02 Oct 2002 18:15:22 -0000
- In-reply-to: <3D9AFB54.80900@ieee.org>
- User-agent: eGroups-EW/0.82

    Dave,

    You bring up a question I had when you mentioned that the
    boundary conditions would take care of themselves. As a newbie to
    FEMM, I'm currently demo'ing Femlab (a finite element analysis
    program that works with Matlab). One thing not covered well in the
    documentation (and not answered yet in an email to support) is when
    certain boundary conditions are applicable such as the "special"
    boundary conditions below.

    > > 1) Electric insulation/continuity: n(dot)J=0, n(curl)H=0
    > > or
    > > 2) Magnetic discontinuity: n(curl)H1=n(curl)H2
    3) Magnetic Potential: Aphi0=Aphi1
    4) Surface current: -n (curl) H = Js

    Will eddy currents (and resulting magnetic polarization) set up in
    the diamagnetic sphere "automatically" be taken care of in femm once
    I switch to AC fields? And off hand, do you know an example for each
    of the above boundary conditions? For instance, doesn't magnetic
    discontinuity above just mean that there is no surface current? So
    far it seems that setting up correct boundary conditions is the more
    difficult part of femm modeling. It doesn't seem clear for different
    materials and situations where one boundary condition is prefered
    over another.

    Anyways, thanks in advance for any help...
    -Scott

    --- In femm@y..., David Meeker <dmeeker@i...> wrote:
    > This ought not to be a big deal to do in FEMM. You wouldn't have
    to
    > apply any special boundary conditions on the surface of the
    diamagnetic
    > particle--it takes care of things itself. Just make sure that you
    > prescribe the right permeability and conductivity for the material
    of
    > the sphere.
    >
    > The one problem that you might run into is a problem of scale. It
    may
    > be difficult to get a good result if you are modeling a coil that
    is
    > several inchs across and simultaneously modeling micron-sized
    particles
    > in the same geometry. You'd be better off to break this into 2
    models:
    > Model just the coil to find the field and the field gradients at
    the
    > point of interest. The size of the domain would be in inches.
    Then,
    > using this info, you could make a second, small problem with the
    > particle and the air around it. The size of the domain would be on
    the
    > order of microns. You'd carefully choose the boundary conditions
    on the
    > edges of the region to give you the "right" field and gradients in
    the
    > absence of the particle.
    >
    > Dave.
    >
    > nortonsm wrote:
    >
    > > 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
    > >
    >
    > --
    > David Meeker <http://femm.berlios.de/dmeeker>

- References:
  - Re: [femm] Forces on a small diamagnetic sphere in an AC/DC field
    - From: David Meeker <dmeeker@ieee.org>

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