Magnetic Field of Current loop around the Core

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Discussion Overview

The discussion revolves around calculating the magnetic field generated by a current loop, particularly when influenced by the presence of an iron core. Participants explore the complexities introduced by the geometry of the material and the implications for magnetic field calculations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant notes that while the magnetic field from a simple coil can be calculated using the Biot-Savart-Laplace law, the presence of an iron core complicates the situation qualitatively.
  • Another participant suggests that if the airgap width is small, the magnetic field in that region can be considered almost homogeneous, referencing Ampere's law for calculations.
  • There is a proposal to use a vector potential approach (B = curl(A)) to address the complexities of the geometry in the magnetic field calculations.
  • A different participant mentions using high precision Biot-Savart calculations and suggests a method involving a 3D compass to visualize the field direction.

Areas of Agreement / Disagreement

Participants express differing views on the best methods for calculating the magnetic field in the presence of an iron core, with no consensus reached on a single approach or solution.

Contextual Notes

Participants highlight the need for numerical calculations due to the complexity of the magnetic field paths in the presence of the iron core, indicating potential limitations in analytical methods.

FelixTheWhale
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Hello friends, I am trying to find how calculate the magnetic field created by current loop considering that there is a some geometry of material that can enhance the magnetic field. I thought it can be solved by multipling by permeability μ but realized that the iron core changes the picture of magnetic qualitatively.

To illustrate this i attached image for: only coil (1) and coil around the iron bar (2).

For the first picture, it is easy to integrate by Bio-Savart-Laplace law, but..
How to find he field for any point at the second picture?

image.jpg


Or, more complicated case:
mm2.jpg
 
Last edited:
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The latter case is easy if the width of the airgap is small ( the magnetic field in the airgap is almost homogenous ).

From Ampere's law you know that
∫ H⋅ds = N*I ( complete circular path )
Also you know that Hiron = μr,iron * Hair

In case of the rod/solenoid, you don't quite know the path of the magnetic field. Some numeric calculation will be needed. ( See my avatar ).
 
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Nice image! What can you advise to make a numeric calculation? Is it possible to apply a vector potential (B=curl (A)) to have the solution for complex geometry?
 
FelixTheWhale said:
What can you advise to make a numeric calculation?
I have used high precision Biot-Savart calculation. Just use a 3D compass and follow the field direction from some point, until the field bites its own tail.
 
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