Mutual Inductance of Coaxial Tube and Coil

• Ian Schwartz
In summary, the conversation discusses working with a Coaxial coil and stainless steel tube to find the mutual inductance. The individual found formulas for the inductance of each separately, but is having trouble with the combination. The issue is that the coil has a current running through it while the outer tube does not, except for eddy currents. The conversation also mentions the importance of end termination, frequency spectrum, tube length, and wire length in the analysis. The type of stainless steel used is also noted as potentially affecting the results.
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!

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?

1. What is mutual inductance?

Mutual inductance is a property of two or more electrical circuits that are in close proximity to each other. It is the measure of the magnetic field generated by one circuit that passes through the other circuit, inducing an electromotive force (EMF) in the second circuit.

2. How does mutual inductance occur between a coaxial tube and coil?

Mutual inductance occurs between a coaxial tube and coil when the magnetic field generated by the current flowing through the coil passes through the conductive tube, inducing an EMF in the tube. This phenomenon is known as electromagnetic induction.

3. What factors affect the mutual inductance between a coaxial tube and coil?

The mutual inductance between a coaxial tube and coil is affected by the number of turns in the coil, the distance between the tube and coil, the diameter of the tube and coil, and the material of the tube and coil. These factors determine the strength of the magnetic field and the amount of magnetic flux that passes through the tube.

4. How is mutual inductance measured between a coaxial tube and coil?

Mutual inductance can be measured using a mutual inductance meter, which measures the amount of induced EMF in the secondary coil when a known current is passed through the primary coil. The ratio of the induced EMF to the current gives the mutual inductance value.

5. What are the practical applications of mutual inductance between a coaxial tube and coil?

Mutual inductance between a coaxial tube and coil is used in various electronic devices, such as transformers, generators, and motors. It is also used in wireless power transfer systems, where the EMF induced in the receiving coil is used to charge batteries or power electronic devices.

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