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,
       I've tried once again to figure out how Etesla6 works by trying
to describe my limited understanding of it to someone who does have a
fairly good knowlege of E&M.  Here is what we think is true, leading up
to what we think is the gap in our understanding...

0. Capacitance = charge per volt, we need to compute the charge on the
    TC (toroid plus secondary) for some given arbitrary voltage on the top.

1. The voltage on the toroid can be chosen arbitrarily and that value
    will be constant across every point on the toroid, and the voltage
    on the secondary can be approximated to be linear from the top down
    to 0 at the base (or a better approximation can come from TSSP).

2. The charge inside an enclosing surface can be computed by summing up
    the strength of the E-field normal to the surface at all points on the
    surface.  This calculation will be independent of the shape or size
    of the surface, in the case of Etesla6 it is a sphere that encloses the
    entire TC.

3. The E-field at any point of the enclosing surface can be computed as
    the (vector) sum of the E-fields from all the points on the surface of
    the object(s) inside the enclosing surface.

4. The E-field at a point on the object(s) inside the enclosing surface
    depends on the charge density at that point.

Minor questions:

? In statement (3) this is independent of whether the line from a point on
   the object's surface to the measurment surface crosses through the object
   or not (we're assuming the object(s) is conductive).

? In statement (3) what if the line crosses significant amounts of dialectric.

Major question:

??? It seemed to us that even though the voltage on the toroid is constant
     across all points on its surface, the charge density would not be, ditto
     for the secondary solenoid. If the charge density is not constant we have
     a major problem computing it (and I think that is the "trick" in Etesla6,
     but I cannot remember what it is), otherwise the above gives a fairly
     straightforward outline of a numerical analysis approach (except that
     even if the charge density is constant across the object surface it is
     not clear what that density would be for a given voltage...).

     I remember the last time I asked you this question I did not really
     follow the answer (something about "shrinking the sphere down to the
     object" in a mathematically smooth way), and my E&M friend could not
     figure it out either.

For me part of the joy of coiling is getting to use my machine shop tools,
part is watching the sparks, and part is learning some new math/physics.
For the later I'ld really like to understand Etesla6 (and someday TSSP too).


thanks,
Peter Lawrence.