Modeling voltage and E-field in teledeltos paper equipotential mapping

[tempneff]

TL;DR

Trying to understand the assumptions behind the use of teledeltos paper to map electric fields

I'm writing a physics simulation to mimic the old equipotential mapping experiment like this one. I can't find much information on how the voltage across this semi-conducting sheet relates to the E-field. Before I start heading down the path sheet resistance and the resistivity of thin-film carbon, I thought I'd ask here.

What are the assumptions that I can make to represent the electrical field lines as voltages across teledeltos paper given a known source voltage and physical dimensions?

 

[Baluncore]

I believe the material is best described as resistive, not semiconductive.
You can assume that perfect conductors are equipotential boundary conditions.

You must decide if you are simulating a finite rectangular sheet, with infinite external resistance, or if you are simulating an infinite virtual sheet.

Will you employ a cartesian grid or a curved orthogonal grid.
Each cell will have a voltage, current magnitude and direction, giving 2D voltage gradient.

Do you have a text that demonstrates the numerical procedure on a cartesian grid ?

 

[Baluncore]

Start here; Electromagnetics, by Kraus and Carver. See section 3.22
There is a copy here; https://www.qsl.net/va3iul/Files/Old_Radio_Frequency_Books.htm

For mapping electric fields, this book is well worth finding;
Analysis and Computation of Electric and Magnetic Field Problems. Second Edition. 1973.
By K. J. Binns and P. J. Lawrenson. Publisher; Pergamon Press.
ISBN 0-08-016638-5

Also;
Title; Electric Field Analysis. 2015.
By; Sivaji Chakravorti. Publisher; CRC Press.
ISBN-13: 978-1-4822-3337-7 (eBook - PDF)

ebooks or files.pdf can be found.

 

[tempneff]

Thanks @Baluncore, that is the oldest pdf I've seen in some time! I think my initial approach was complicating an easy problem. The lab assumes that the paper is lossless and that the charge distribution matches the electric field created by the electrodes. For the Point-source case (circular electrodes; simulated map voltages, real map voltages, and a simple kq/r calculation all agree. Why? That I'm not sure of.

 

[tempneff]

I should have mentioned, that this is a low fidelity simulation for university undergraduates to play with online.

 

[The Electrician]

Would you like some teledeltos paper?

https://en.wikipedia.org/wiki/Teledeltos