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# Re: Direction of Flux

- To: femm@yahoogroups.com
- Subject: Re: Direction of Flux
- From: "David Meeker" <dmeeker@ieee.org>
- Date: Thu, 10 Apr 2003 15:52:04 -0000
- In-reply-to: <b73u7d+l2f7@eGroups.com>
- User-agent: eGroups-EW/0.82

    --- In femm@yahoogroups.com, "tano1938" <rgarritano@c...> wrote:
    > I'm a new user, so please be kind and patient.
    >
    > What is the direction of B in the tutorial sample problem #1? If I
    > use the equation B=curl(A), it seems that it is normal or comes out
    > of the page. If I go by the statement in the manual that the "normal
    > flux (normal to a boundary) is equal to the tangential derivative of
    > A along a boundary," then it seems to be in the Y direction (since in
    > this example, A has a derivative only in the x direction).
    >
    > Thanks for your help.

    Let's restrict ourselves to 2D planar problems for the moment. In
    this case, A is actually a vector in which a positively directed A
    points up out of the page at you. If c1, c2, and c3 are unit vectors
    along the x, y, and z axes respectively, and a is the amplitude of A,
    we could say:
    A = a*c3
    Flux density is the curl of A, which is the determinant of the matrix
    {{c1,c2,c3},{d/dx,d/dy,0},{0,0,a}} (since this is a 2D planar problem,
    a lot of the entries in the matrix are zero). Evaluating the flux
    density gives:
    B = da/dy * c1 - da/dx * c2
    All of the flux flows in directions that are normal to A and in the
    plane of the screen. For axisymmetric problems, things are
    conceptually similar, although the math is a bit messier.

    --- In femm@yahoogroups.com, "tano1938" <rgarritano@c...> wrote:
    > I'm still having problems visualizing the vector potential boundary
    > field in the first example in the tutorial. Can someone give me an
    > example of a device that generates this field, i.e battery, current,
    > coil, etc. The second example is fine as one can easily build it in
    > a laboratorty and test the results.

    The boundary conditions in the first one are sort of an artifice
    devised to make an even magnetic field w/out having to explicitly
    model some physical device that is a source of the field. I've seen
    people do this "explicitly" by first modeling a long air-cored
    solenoid, this yields a relatively constant field in the middle of the
    solenoid. The object of interest are then placed in the middle of the
    solenoid. This approaches the same results as when the field is
    produced by setting the boundary conditions when the boundaries are
    placed increasingly far from the objects of interest.

    (N.B. for "advanced users": I think that the "best" way to model this
    situation in a 2d planar geometry is to model two circles that are
    connected together using periodic boundary conditions--just like when
    using the Kelvin transformation to model an unbounded region. Then,
    fill the circle representing the exterior region with a unit
    permeability material with Hc set to be equal to twice the H that is
    desired in the uniform field region. Place the objects of interest in
    the other circle, representing the interior region. The objects of
    interest are then exposed to a uniform magnetic field, but the total
    flux is not defined a priori (whereas it is with the set BC case).
    Also, perturbations to the uniform field due to the presence of the
    objects of interest aren't influenced be the presence of nearby
    "artificial" boundaries. See
    http://groups.yahoo.com/group/femm/files/demo1a.zip as an example of
    the implementation)

    Dave.
    --
    David Meeker
    email: dmeeker@ieee.org
    www: http://femm.berlios.de/dmeeker

- References:
  - Direction of Flux
    - From: "tano1938" <rgarritano@comcast.net>

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