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Re: Flat conductors



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