# Coaxial coils in dielectric material

1. May 29, 2012

### orcaja

Hi everyone

I have a problem to solve, I already simulated it with FEMM, but I wonder if it is possible to find an analytical solution.

Let's say that there's a small coil (100 turns) around a pipe (2in diameter), the pipe is filled with air.
This pipe is located inside a bigger pipe (8in diameter), which also has a coil similar to the first one (100 turns), the two coils are aligned (coaxial). Outside of this pipe there is air.

The space between the two coils is filled with two layers of different diamagnetic materials.

The outside coil is excited with an ac signal, (let's say 1Vpp, 100kHz).
Neglecting the effect of the pipes, (i.e. just taking into account the effect of the diamagnetic materials, and the air) How can I calculate the induced voltage in the inside coil?

I'm really a beginner, but willing to try everything, right now I'm having a look at the book
classical electrodynamics by David Jackson, but I still don't have an idea how to solve it.

Any advice is very welcome.
Thanks in advance.

2. Jun 1, 2012

### marcusl

Diamagnetism is such a weak effect that it can be ignored in this case. Your problem devolves to the coupling between two coils in a vacuum. The mutual inductance between two short coaxial solenoids is available in many places; Grover's old book Inductance Calculations (or something like that) is a good place to look for the answer, other texts will give you the derivations.

If you are really a beginner, as you say, than stay away from Jackson, which is a graduate level physics text. How much of a beginner are you? Have you studied vector calculus and freshman physics? Then Griffith is the classic physics text to look at. For EE's, Balanis's book on E&M is a standard. If you haven't gotten that far, then start by studying calculus (including vector calculus, Gauss's and Stoke's theorems, etc.) and a freshman physics text like Halliday and Resnick before moving up.

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