I'm doing an experiment where I'm trying to determine the conductivity of a material by putting a sample rod in the center of a coil which is a part of an RLC circuit with an AC generator.
I was told by certain professionals in the field that putting the rod inside the coil will have an effect of extra resistance in the circuit (non inducitve thermogenic resistance). Now, I've already tried to do the experiment once, and I confirmed this.
Although, I was also told that this extra resistance, or so-called contactless resistance (the rod doesn't make contact with the coil), will take the form of R=λ*sqrt(ω) ; (only for high frequencies, for relatively low frequencies of around 60Hz, R is proportional to ω²) where ω is the angular frequency of the AC generator, and λ is a constant dependent on the conductivity of the sample rod and certain parameters of the coil
Specific form of λ: λ=(L0a/b²) sqrt(2/μ0*σ) ; L0 - inductance of the coil without the sample rod inside it ; a- radius of the rod ; b² ( it's written as b with a line above it, then all of it squared, I just can't write that here. Apparently that's just how the symbol for that parameter is written, nothing is really being squared here) - another parameter of the coil itself ; μ0 - magnetic permeability of a vacuum ; σ- specific conductivity of the sample rod material
Does anyone know of any scientific papers with the theory behind this or why contactless resistance takes this form? It's clear that the form of λ is reminiscent of the formula for skin depth with skin effect, but nothing really beyond that.
Also, while I was performing the experiment I found that one major problem was getting over the skin effect inside the coil itself. The frequencies of the generator were so high (recommended for them to be so for the best results) that the thermogenic resistance of the coil became a significant factor, in fact even more signifacnt than the contactless resistance. In fact, once we performed the experiment, but just without any sample rod inside the coil, the results showed a linear graph of the dependence of thermogenic resistance of the circuit on frequency. Do you have any suggestions on how to get over this? How can I remove the skin effect on the coil and just have the contactless resistance coming from the eddy currents inside the rod?
