re: Re: Etesla6 math questions

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

Original poster: "Peter Lawrence by way of Terry Fritz <teslalist-at-qwest-dot-net>" <Peter.Lawrence-at-Sun.COM>

Terry,

The book "field solutions on computers" looks like it might fit the bill.

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.

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.

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!)

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.
 >
 >