Electrical Resistance between 2 points in homogeneous plane?

[memoguy]

Hi there!

Just say I have large square piece of some homogeneous resistive material like graphite. How would I go about determining the resistance between any two given points?

Further, just say I supply a voltage across two arbitrary points, can I determine the voltage difference between any other two arbitrary points?

I don't even know where to begin with this.

 

[nasu]

See Kelvin probe or four point probe for the measurement of resistance and resistivity.
http://en.wikipedia.org/wiki/Four-terminal_sensing
You can also use two point probe, where you measure the current in the external circuit and the voltage between the two points. The ratio V/I will be the resistance between the two points.

About calculating the voltage between other two points, it can be done but it is not trivial. You will need to do some finite element analysis of your system.
It depend on the geometry of the sample and probe.