If I have a copper sheet, some rectangle say, and I connect opposite diagonal corners to a battery (naturally with a resistor in there) then can one calculate the current flow at different points in the sheet?

How could one calculate the current moving past some arbitrary point? Can one treat this as some kind of resistor array? can we use calculus to determines some kind of function here?

The problem is discussed here a bit too:

https://www.physicsforums.com/threads/current-through-flat-sheet-or-plate.1048113/

 

Look up FEA (finite element analysis).

 

If I have a copper sheet, some rectangle say, and I connect opposite diagonal corners to a battery (naturally with a resistor in there) then can one calculate the current flow at different points in the sheet?

How could one calculate the current moving past some arbitrary point? Can one treat this as some kind of resistor array? can we use calculus to determines some kind of function here?

The problem is discussed here a bit too:

https://www.physicsforums.com/threads/current-through-flat-sheet-or-plate.1048113/

For some reason I am just seeing this now.

I had used partial differential equations to solve this using resistor arrays. I went up to some 10000x10000 resistors.
The result looked like a solution to the Laplace Equation. That distribution is probably shown online somewhere.
This means the Laplace Equation would come from this if the number of resistors on one side was allowed to go to infinity.

Although the results are interesting, there may be interactions between the electrons themselves which is not considered in the resistors array model. Of course whether or not that matters is a question I did not look into.