re: Re: Etesla6 math questions

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Terry Fritz" <teslalist-at-qwest-dot-net>

Hi Peter,

At 08:26 PM 1/31/2003 -0800, you wrote:
>Terry,
>
>The book "field solutions on computers" looks like it might fit the bill.

Yes, any of those books will fully explain it all.  I was hoping for a nice 
on-line (free) source since those books are not cheap.  But there is always 
the library too.


>But I'm still confused since I have a (perhaps incorrect) notion that what
>you mean by "relaxation thing" is "successive over-relaxation" aka SOR.
>My recollection of SOR is that you can use it to compute the values of a
>field within some region if you know values on the region's boundary and
>a differential equation that relates the field values at neighboring points.

Yes, that is what it does.  Boundary conditions are set up and all the 
points are averaged over and over until it stops changing.  Then all the 
points in the matrix will have the right voltage.


>The example I remember is temperature calculation on a plate with fixed
>temperature heat sources and sinks along the edge, and I can see a loose
>analogy with gaussian surfaces. It seems to me that in our case the "region"
>is the space between the enclosing surface and the TC inside it, and the
>"boundary" is both the surface and the TC.

There are many applications of the basic idea.


>Since we are trying to compute the field on the TC, and it is a required
>input for SOR since it is actually part of the boundary, it seems like we
>are SOL (sorry!)

We know the voltages of the coil and distribution (thanks to Paul), so we 
have all the boundary conditions we need.  We just have to crunch the 
numbers and figure out the resulting flux.

Cheers,

         Terry



>thanks,
>Pete Lawrence.
>
>
>
> >Original poster: "Terry Fritz" <teslalist-at-qwest-dot-net>
> >
> >Hi Peter,
> >
> >A goggle search for "e-field calculation equipotential" brings up many fine
> >sources like:
> >
> >http://www.electrostatics3d-dot-com/Main/Home.htm
> >
> >http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html
> >
> >http://www.fieldp-dot-com/book.html
> >
> >http://www.electrostatic-dot-com/Humphries.htm
> >
> >but these are all too "high brow"....  the "real" method is trivial...  I
> >don't seem to find a "straight forward" on-line explanation for how one
> >finds the E-fields in a 2D space with boundary conditions....
> >
> >I am hoping one of our more learned people out there has that perfect
> >explanation?  All it does, is the computer averages the four points around
> >a given point many many times...  Seems so simple but I can't explain it
> >with words...  Let me think on the explanation and hope someone else has
> >the answer in the mean time ;-))
> >
> >I hate to be the blind one leading the blind here 8-))
> >
> >Cheers,
> >
> >         Terry
> >
> >
> >At 06:44 PM 1/31/2003 -0800, you wrote:
> >>Terry,
> >>       here is the part I did not understand the first time around and 
> still
> >>don't understand:
> >>
> >>
> >> > The charge density certainly is non-uniform.  But that is controlled by
> >> the
> >> > shape and E-Tesla does the "E-field relaxation thing" to find the 
> E-field
> >> > (voltages) around the coil.
> >> >
> >> > When we do the relaxation matrix, the charge density on the parts works
> >> > out!!  Sharp edges get high fields do to high densities.  Smooth 
> edges get
> >> > low fields do to low densities.  The "relaxation" does this field 
> density
> >> > adjustment for us.
> >>
> >>
> >>where can I read about the "relaxation thing", this seems to be the crux of
> >>the matter. It seems to be a well known numerical analysis of fields
> >>technique, but I've never taken more that an introductory numerical 
> analysis
> >>class and have not heard of this, and it might be a bit more involved than
> >>you could describe in email...
> >>
> >>
> >>thanks,
> >>Pete Lawrence.
> >
> >