Assume you have a rectangular bar of copper with finite length L. You apply a voltage difference at two points on the top surface of the bar; (x1,y1) and (x2,y2). Because the bar is finite in length, I believe that the current will not be uniformly distributed. How would you go about calculating the voltage and current density at an arbitrary point within the bar?
I have tried to think through a few models that would approximate this, but I keep falling short. I think there must be a better way. Ideally, there would be an actual equation that I could derive that would give me the voltage and current density at any point within the bar. I have also wondered if a finite element method approach is best here.
If the bar is relatively thin in the z direction, I wonder if the problem can be simplified by instead considering a copper sheet with no thickness.
If anyone could point me in the right direction, I would really appreciate it.