I am trying to calculate analytically the cell constant of my probe. I am aware that the standard procedure is to get a fluid of known conductivity, make a conductance measurement and divide the two to get the cell.

I am not interested in this technique, since I need to it analytically.

My probe is coaxial. It means that it has a wire in the center and is surrounded by a conductive cylinder. The signal is applied on this central wire and the cylinder.

I am trying to calculate the cell constant using the formula κ = σ/G, where:

κ is the cell constant,

σ is the resistivity,

and G is the conductance.

What I have so far is that G = I/V.

I can calculate the V from the electric field inside the coaxial probe. It is the well known expression V = λ*ln(r2/r1)/(2*π*k*ε0), where:

λ is the linear charge distribution,

r1, r2 are the radius of the coaxial cable,

k is the dielectric constant of the sample that I want to measure

and ε0 is the electrical constant of free space.

To sum it up I am stuck in finding I. It can also be the case that my thinking process is wrong from the beginning, so please point me towards the right direction.

Thank you very much for your time and help.