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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: Fri, 04 Oct 2002 18:39:39 -0000
- In-reply-to: <3D9C4F97.4080905@ieee.org>
- User-agent: eGroups-EW/0.82

    Dave,

    Thanks again for the help... This program is really fun! I had a
    question about calculating forces in axisymmetric problems. By
    looking over the past archives I found a couple references to this
    (how one should start and end the contour on the r=0 axis). With
    respect to your "ball" example. Let us say there is an
    axisymmetric "r" component to the magnetic force (rather than being
    uniform). I'm interested in calculating the forces in both z- and r-
    on the ball. i.e. in the case where the ball is diamagnetic there
    should be an "r-" restoring force and a positive "z-" suspension
    force on the ball. However, in the axisymmetric problem the r- force
    would (and should (I havent checked)) turn out to be zero. Is there
    a way to determine the "r- component" restoring force? (even though
    its zero right at the r=0 position). I guess I want the second
    derivative of the radial force (d2F/d2r). How do I calculate that in
    femm and are there "things to watch out for" in terms of the
    calculation?

    Thanks!!!
    -Scott

    --- In femm@y..., David Meeker <dmeeker@i...> wrote:
    > "nortonsm" <nortonsm@y...> wrote:
    > > 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?
    >
    > Yes.
    >
    > > 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.
    >
    > You generally never have to apply any of those boundary
    > conditions--internal boundaries always "take care of themselves."
    For
    > example, 1) is never an issue, because in the 2-D formulations, all
    > current flows in the into-the-page direction. (You can, however,
    set up
    > constraints on the total current carried in a set of regions to
    define
    > how they are hooked together). Number 2) , by which I think that
    you
    > mean that the part of H that is tangential a boundary should be
    > continuous across the boundary, gets enforced "automatically"
    because
    > this is a property of the vector potential formulation and the type
    of
    > elements used. (To be really strict and use the correct
    terminology, it
    > is automatically "weakly" enforced). 3) Again, this is imposed
    > automatically by the finite element formulation. Since the nodes
    are
    > always made to line up along boundaries, and the boundary nodes are
    > members of elements on either side of an interface, you get
    continuity
    > of A automatically. With 4), I haven't implemented surface
    currents on
    > internal boundaries. You have to either define currents over a
    finite
    > (but possibly very thin) area, or define point currents. Surface
    > currents on the edges of a domain can be defined the "mixed" type
    of
    > boundary condition (corresponds to the c1 parameter), but I'd say
    that
    > people almost never do this.
    >
    > Typically, you just have to define boundary conditions explicitly
    on the
    > outer boundaries of the domain. Most often people are interested
    in
    > objects that are surrounded by free space. In this case, it is
    > generally sufficient to define a solution region that is somewhat
    bigger
    > than the object that you are interested in and define A=0 all
    around the
    > edge of the solution region. You can do more elaborate boundary
    > conditions if you want to exploit symmetry, periodicity, or do a
    slicker
    > approximation of an unbounded domain.
    >
    > As an example, see the attached problem. This is supposed to be an
    iron
    > ball sitting in a spatially homogeneous field of amplitude 0.1 T
    that
    > varies at 1 Hz. The problem domain looks like a cylinder with the
    ball
    > in the middle. The only boundary condition I had to define was a
    fixed
    > A boundary condition for the outer edge that sets the flux in the
    > domain--I've seen other people do this sort of problem by
    explicitly
    > modeling a coil that produced the field and assigning A=0 to a far
    away
    > boundary, which is an equally valid approach. Anyhow, you can see
    you
    > the interface between different permeabilies, the induced currents,
    and
    > their reaction field, all sort themselves out.
    >
    > Dave.
    > --
    > David Meeker <http://femm.berlios.de/dmeeker>

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