# [Getdp] Magnetic Force 3

Kubicek Bernhard Bernhard.Kubicek at arsenal.ac.at
Fri Aug 11 11:20:18 CEST 2006

I would guess that the PostIntegration example in the wiki might help you:
http://www.geuz.org/getdp/wiki/PostIntegration

With this info there a body force term could be somehow like:

{ Name F ; Value { Integral { [ 1/mu0*({Curl h} /\{h}) ] ; In Body ; Jacobian Vol; Integration Int; } } }

Maybe the problem is that if you have a magnet, you define a constant field inside, that is not altered by the outside field. So inside, there is no acting from outside, and hence no force.

A collegue of mine just showed my a formula developed through the stress tensor:

F_surface=\int_Face ( 1/mu0*(df.b)*b ) - \int_Face ( 1/2*1/mu0*(b.b)*df )

with the df being a vector normal to the face and . being the inner product.
Maybe you can do this for all faces or you magnet and add the values manually:
{ Name F ; Value {  Integral {
[ 1/mu0*(Vector[0,0,1]*{d phi}*{phi})
-1/2*1/mu0*Vector[0,0,1]*(( {d phi}*{d phi}) ] ;
In SurfaceXY; Jacobian Sur; Integration Int;
} } }
But, honestly, thats just guessing. Also, I don't really understand what your physical system.
What i just found in the manual, is NormalSource

{ Name FTotal ; Value {  Integral {
[ 1/mu0*(NormalSource[]*{d phi}*{phi})
-1/2*1/mu0*NormalSource[]*(( {d phi}*{d phi}) ] ;
In MagnetSurface; Jacobian Sur; Integration Int;
} } }

nice greetings, bernhard

-----Ursprüngliche Nachricht-----
Von: getdp-bounces at geuz.org [mailto:getdp-bounces at geuz.org] Im Auftrag von Jasper
Gesendet: Donnerstag, 10. August 2006 20:20
An: getdp at geuz.org
Betreff: [Getdp] Magnetic Force 3

Thank you for your reply. From what I gather your problem involves moving charges in a magnetic field, for which the Lorentz force for a volume can be written as

F = qv x B

>From what I gather this can be rewritten to a form, where for a
magnetostatic problem, the force can be expressed only in terms of the magnetic field:

f = 1/mu0 * ( B x ( Curl B ) )

My problem (so far) only involves a magnetic field from a permanent magnet, thus from calculations I only obtain the scalar potential H (as in the examples on the wiki). From H I obtain B and phi in post-processing. Now I'm wondering how to obtain F. Thanks for your reply. I have to look into this some more.

Jasper

On 8/4/06, Kubicek Bernhard <Bernhard.Kubicek at arsenal.ac.at> wrote:
> I calculate a Lorentz Force density in the Postprocessing by the
> following expression (having a temperature-field-dependent
> conductivity):
>
>
> { Name f ; Value { Term { [ con[{T}]*({Curl a} /\{d v1})] ; In Vol ;
> Jacobian Vol; } } }
>
> This works in my case.
>
> Maybe this helps you,
> nice greetings from rainy Vienna,
> Bernhard Kubicek
>
>
> -----Ursprüngliche Nachricht-----
> Von: getdp-bounces at geuz.org [mailto:getdp-bounces at geuz.org] Im Auftrag
> von Jasper
> Gesendet: Donnerstag, 3. August 2006 23:01
> An: getdp at geuz.org
> Betreff: [Getdp] Magnetic Force 3
>
>
> Hi,
>
> I've used a scalar potential to calculate the field in a 3D
> magnetostatics problem. Looking at the fields the results look correct. Now I would like to calculate the force on a object due to this magnetic field.
> >From what I can gather from the mailing list several people have
> already done this before, but I have yet to find any examples. It
> appears the force can be calculated in three different ways:
>
> - Take the B-field, and compute 1/mu0 * B x ( Curl B ) over the
> volume. This is probably easiest achieved in PostProcessing or Gmsh, but somehow the Curl B of my field in Gmsh returns zero...
> - Compute the Maxwell Stress Tensor using the B-field, and integrate it over the surface of the object. This is probably best performed in PostProcessing, but I'm at loss on how to go from the B-field in the element volumes to the field at the surface of the object.
> - Using Virtual Works. No idea how to do that, but it probably involves small displacements :-)
>
> If anybody can show me some examples of computing these quantities it
> would be very much appreciated. Thanks in advance for your help. Best
> regards,
>
> Jasper
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