Re: I need help.

[Bernard Cleyet <anngeorg@PACBELL.NET>]

Something I think related and explained by the below.

One of my references pointed out that the resistance between two embedded
electrode spheres in the earth (rather more closely infinite embedding
medium) was ~ independent of their separation > a certain minimum
separation.  --IF I REMEMBER CORRECTLY.

bc


Roger Haar wrote:

> Hi,
>         What I think is wrong with your claim is your
> assumption that between two points, the resistance
> and the current paths have the same sensitivity.
> The current path is the analog to field lines and
> is related to the equipotentials.
>
>         Consider the case where the two terminals are on
> a horizontal line. and consider a current path
> that starts out from the right terminal headed
> almost to the right.
>
>         In the infinite case, this path is extremely long
> and has a very high resistance and has little
> effect on the total resistance.
>
>         In the finite case, this path is "distorted" and
> shorter, but the current path is effectively
> squeezed together with other paths.  The effect of
> the squeeze is that each current path has less
> width and thus a higher resistance.  The combined
> effect is that this current path has only a small
> effect on the total resistance.
>
>         Thus the current paths and the associated
> equipotentials can be very different between the
> finite and the infinite, but the resistances can
> be almost the same.
>
> ***********
>         Am I correct in understanding that in you
> measurement of resistance as you cutdown the sheet
> that the rings were 2.5 cm apart at the closest
> point.  The near points dominate the resistance.
> Look how much of the rings is within 5 cm of each
> other.  One would be tempted to consider this a
> distorted parallel plate capacitor  The 2.5 cm
> separation is much smaller than the paper.  If I
> draw this and add a few current paths, and then
> start "cutting down" the sheet, there are not that
> many paths that get cut.
>
> ***********
>         I am confused by your term "surface charges."  In
> the resistor-paper analog to electrostatics,
> charges become current sources or sinks.  Are you
> saying that along a given ring,  the voltage is
> not functionally constant, i.e. the resistance of
> the silver paint is noticeable relative that of
> the paper?
>
> Thanks
> Roger Haar
>
> **********************************************************
>
> kowalskil wrote:
> > But what is wrong with my claim that the finite size of the sheet
> > has a negligible effect for the geometry chosen? Is it not true that
> > rho calculated from your formula, David, and rho calculated from
> > the narrow strip would be different if a sizable fraction of the total
> > flux was prevented from going through regions outside the paper?
> > The two values of rho turned out to be practically identical. How
> > can you ignore this argument?
> >
> > I will ask students to locate the experimental curves for a geometry
> > in which circles are closer than 10 cm. If the discrepancy between
> > what is observed and what is predicted is reduced then I will also
> > start blaming the paper size effect. We will see. For the time being
> > I will blame surface charges. I know that such blaming has no value
> > unless some theoretical or experimental evidence is produced. I think
> > I do have some evidence against the paper size effect. Where am I
> > wrong with it?