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Re: Flat conductors



Another try in plain text (which will destroy the equations)

Again, Harnwell discusses leaky caps. pp. 105 ff.

(1) An appropriate result is the surface charge density at the interface
of two sheets: qs = k0*ivn(k1/sigma1 - k2/sigma2)

where ivn is the normal component of the current density

(2) from D2 dot ds - D1 dot ds = qs ds (Gauss's law and the theorem of
flux)

"We know how the equipotential lines would look like in a perfect (no
leaking) capacitor. In that case the equipotential lines would not bend
suddenly at the horizontal boundaries of the five carbon strips."


Aux contraire; (thought maybe not of which LK is thinking) on p. 69
Harnwell gives the angle of refraction of lines of force across the
interface of two dielectrics (conductivity zero) as:

(3) k1 COT (theta1) = k2 COT (theta2)

(3a) I suspect for leaky dielectrics it's k/sigma. (He doesn't even
leave this as a problem for the "student."

bc who's great at quoting Harnwell, but not much else.

P.s. To confirm LK's result, (I suspected his "ersistors" were not
making good contact with each other and the full Pasco sheet, which I
found partially true) I tried gluing them together w/ C-dag (C in
isopropyl alcoho;l). Where the "glue" succeeded, I obtained his result,
but in a coupla cases the strip was not glued and I obtained a different
result when I pushed the two (strip and full sheet) together. Since
the C-dag doesn't incorporate a glue, (the Ag-dag does), I tried
painting a strip with the C-dag. (Acheson DAG 154 sold by
Sargent-Ewlch). Except for non uniformity I found, as expected, the
refraction. I may, eventually, check out (3a) on my strip.





Ludwik Kowalski wrote:

P.S.
The top setup (five parallel resistors glued to a Pasco sheet)
can be viewed as a very leaky capacitor. We know how the
equipotential lines would look like in a perfect (no leaking)
capacitor. In that case the equipotential lines would not
bend suddenly at the horizontal boundaries of the five
carbon strips.

Ludwik Kowalski wrote:

Yesterday I wrote:

.... I have a new set of equipotential lines to share.
But this deserves a separate message.

You can see that message by clicking on the URL below.

http://blake.montclair.edu/~kowalskil/elec/strip1.html

If your system does not allow jumping to my website
directly then go to your favorite browser and access the
above URL from there. Comments and suggestions, as
always, will be appreciated. Please verify my observations.
Ludwik Kowalski