re Field variation with configuration (was re Conferring..)

[brian whatcott <inet@INTELLISYS.NET>]

> Chuck Britton asked:
>
> > One object could be the usual charged point particle and the
> > other could be a charged non-conducting ring? Wouldn't THAT
> > satisfy Ludwik's point?
At 09:22 7/1/01 -0400, Ludwik wrote:
> In my opinion the answer is NO. If the 1/r^2 laws are valid then
> the magnitude of the net electric force is equal to the magnitude
> of the net gravitational force at any distance, even when the
> point-like particle is in the center of the ring (0=0).
> Ludwik Kowalski


Mmmm....pity. Denker offered a moment of nirvana not too long ago
with a very general insight into the form of fields to be expected
from points, lines and flat areas.

It went something like this:
 Consider some space filling effect emanating from a point.
You would expect it to be diluted acording to the surface of the
sphere at your radial distance from the singularity. 1/r^2

Consider some space filling effect emanating from a line.
You would expect it to be diluted acording to the length of
the circumference of a disk at your radial distance from the
singularity. 1/r

Consider some space filling effect emanating from a flat surface
of very large extension, compared to your distance.
You would expect it to be undiluted at any (moderate) distance.

You will notice that the assumption here is Aristotelian space.
I fancy more developed space structures would yield a comparable
rule.

Armed with this insight, if I suppose a particle's trajectory to be
axially towards a ring of radius r at a distance d from its center,
 I expect the force to vary as 1/(sqrt[r^2 + d^2]) to support
the 1/distance force expectation. This has extremes of 1/d and 1/r
while the particle is on axis.


brian whatcott <inet@intellisys.net>  Altus OK
                Eureka!