Electromagnetism: Magnetic Field, change in permeability

[Helmholtzerton]

Hello everyone.

I've built a Helmholtz coil and I'm attempting to understand how the magnetic field direction and magnitude will be effected do to a material with a particular permeability.

In the first picture I have an infinitely long cylinder with a particular thickness and permeability. There is a coil around the chamber. My Helmholtz coils are some distance from the chamber. I'm trying to find out how the B or H field is effected by the chamber due to its permeability and thickness. There are three areas that I'm concerned about. I was able to solve this for the center of the coil without the chamber using Biot Savart. I'm not sure what happens when a material is added in between.

In the second picture I have an infinitely long piece of square strut. The is a coil around the strut. The strut is off center to the coil. The strut has a particular height and width. I'm trying to find out how the be field is effected within the coils due to the piece of strut.

Is there a particular section in Jackson or Griffiths that would help me understand this problem? I'm assuming dB/dt = 0 as my coils have been turned on and running for some time.

Thanks to anyone who could provide some insight to this problem.

 

[mfb]

The cylinders in the sketch have infinite length, the coils do not (just two with zero length each)? I'm quite sure that needs a numeric simulation.

 

[Helmholtzerton]

Assume just one coil in a plane. I'm pretty sure this will require a numeric simulation as well.

I found an example in Jackson that gives some insight to this problem. I have a CAD model of this. Is there is a free solver somewhere for a problem like this?

 

[Omega0]

Have you access to any code solving the Laplace equation in 2D?
You should as a student. I can give you links if you need.