Resistivity calculation from two-probe resistance measurement of sheet

[no_einstein]

Homework Statement

You make a two-probe resistance measurement (probe spacing S) of an infinite sheet (thickness t) of a high-resistance material. How do you calculate the resistivity of the material?

Relevant Equations

R = ohm, rho = ohm*m

I'm really not sure. Obviously I can get the units right with Resistance * thickness, but I assume there's a correction factor here that I can't find anywhere?

 

[kuruman]

There was considerable discussion about this almost 9 years ago here which you might find useful.
https://www.physicsforums.com/threa...-two-point-voltages-on-infinite-plane.832960/

 

[haruspex]

I studied this once out of my own interest. I concluded that as stated in post #1 it makes no sense. What you also need to know is the perimeter of each contact area. With point contacts the theoretical resistance is infinite.
If we take those areas to be elliptical, we can have an exact solution with nested elliptical equipotentials around each contact ellipse. The 'central ellipse', i.e. where the one family transmutes into the other, is the perpendicular bisector of the two contact areas. The potential at any point is proportional to the logarithm of the ratio of distances to the 'centres', i.e. where the two families of ellipses would shrink to zero.