Mutual Inductance of Coaxial Tube and Coil

[Ian Schwartz]

In my lab we are working with a Coaxial coil and stainless steel tube, and are aiming to find the mutual Inductance. I've done some looking around and have easily found the Inductance of a Coaxial cable, and for that of Coaxial coils, but am having trouble with a combination of the two.

The catch is that our coil has a current running through it, while our outer tube does not except that due to Eddy currents.

For two Coaxial coils, the mutual Inductance formula I found was:

M = μ*n1*n2/(π*(r1)^2) where n = N/l

While for the Coaxial cable it was:
L/l = μ/(2π)*ln(r1/r2)

To clarify, we have a coil with a current inside of a conducting tube. I would like to know the Inductance here. Can anybody point me in the right direction to solve this in our set up?

Thanks!

 

[Baluncore]

Welcome to PF.
A coil inside a conductive tube will “see” it's reflection from the inner surface of the tube. So the tube will appear to be the mirror image of the coil. The eddy currents will be the reflection. The current will be reversed in the image, so the combination becomes a differential transmission line, a transmission line transformer or a current transformer.

The details of end termination (to the tube) will be critical in analysis of the transmission line model.
Also, the coil current frequency spectrum, the length of the tube and the length of wire in the coil will be important.
Stainless steels are not always well behaved at radio frequencies, some are magnetic, some not. What grade of stainless steel is used?