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

- To: femm@yahoogroups.com
- Subject: Re: [femm] Forces on a small diamagnetic sphere in an AC/DC field
- From: David Meeker <dmeeker@ieee.org>
- Date: Wed, 02 Oct 2002 09:57:40 -0400
- References: <anbh5m+665g@eGroups.com>
- User-agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.1) Gecko/20020826

`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>

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    - From: "nortonsm" <nortonsm@yahoo.com>

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