Electromagnetism: Magnetic Field, change in permeability

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Discussion Overview

The discussion revolves around the effects of material permeability on the magnetic field generated by Helmholtz coils, particularly when materials of different shapes and properties are introduced into the magnetic field. Participants explore theoretical and numerical approaches to understanding these effects, focusing on specific configurations involving cylinders and struts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant describes a setup involving a Helmholtz coil and an infinitely long cylinder with specific permeability, seeking to understand how the magnetic field (B or H field) is affected by the cylinder's properties.
  • Another participant notes that the coils are not infinitely long, suggesting that numerical simulation may be necessary to accurately model the situation.
  • A third participant proposes that a single coil in a plane may also require numerical simulation and mentions finding an example in Jackson's work that provides some insight.
  • One participant offers to share resources for solving the Laplace equation in 2D, indicating that such tools may be useful for the problem at hand.

Areas of Agreement / Disagreement

Participants generally agree that numerical simulations are likely necessary to address the complexities of the problem, but there is no consensus on the specific methods or resources to be used.

Contextual Notes

Participants express uncertainty regarding the effects of material properties on the magnetic field and the need for numerical methods, indicating that analytical solutions may not be straightforward in this context.

Who May Find This Useful

This discussion may be useful for students and researchers interested in electromagnetism, particularly those exploring the interactions between magnetic fields and materials with varying permeability.

Helmholtzerton
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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.
 

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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.
 
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?
 
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.
 

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