What happens when electric current is distributed in the material?

[Another]

TL;DR Summary

What happens when electric current is distributed in the material(Non-metal)?

When supplying electricity to the material. the shape of the material may or may not be square.
This material may be

This material may be moisture materials or solid materials that may conduct electricity.

I would like to know the travel characteristics of electric currents and the potential difference in each position of the material.
How will be distributed?

Is there a topic or theory that explains this behavior? Please advise me to study.

 

[alan123hk]

I believe that the vector form of Ohm's law in combined with Ampere's circuital law can be applied.

J = σ E

where J is the current density at a given location in a resistive material, E is the electric field at that location, and σ (sigma) is a material-dependent parameter called the conductivity

 

[Svein]

Summary:: What happens when electric current is distributed in the material(Non-metal)?

I would like to know the travel characteristics of electric currents and the potential difference in each position of the material.
How will be distributed?

Well, that depends on the state of the material and the environment. A research institute I worked for 40 years ago used this principle for detecting internal cracks in oil pipes. You run a high current through the material and measure the magnetic field between the poles (the current and the field will "wrap around" any cracks).

 

[anorlunda]

Summary:: What happens when electric current is distributed in the material(Non-metal)?

I would like to know the travel characteristics of electric currents and the potential difference in each position of the material.
How will be distributed?

That's not a simple question. By the way, you have a 3D object, not 2D.

Semiconductor device designers consider exactly that question. For example:

There are also analytic methods as in
https://www.google.com/url?sa=i&sou...aw19xF9WbQbgd0CFFKQrv87b&ust=1576769471286070

https://www.google.com/url?sa=i&sou...aw19xF9WbQbgd0CFFKQrv87b&ust=1576769471286070

If the external voltage is not constant in time, there are also eddy currents, surface currents, and transient solutions to consider. This is no simple answer to your question. I expect that many PhD theses have been written on that question.

 

[Lord Jestocost]

I would like to know the travel characteristics of electric currents and the potential difference in each position of the material.

One way to approximately get such data is an equivalent circuit simulation by modelling the material as a 3D resistor network.

 

[Baluncore]

A point has no area so the resistance of a point contact is infinite. The current density at a point contact is also infinite. While voltage measurements can be made at points, the current density pattern in a resistive material must be specified between defined contact areas, not between point contacts.

Analytic solutions require restriction of the contact areas and boundary conditions to idealised geometry.

Electric field patterns and current flow in real-world bounded-solids are often solved using finite element numerical relaxation techniques.