# Do ferromagnetic materials do "spatial averaging"?

• GaryLS
In summary, the linear amplification model of field strength within ferrite does not appear to be correct. It appears that there is some sort of spatial averaging going on, leading to an incorrect understanding of the field strength.
GaryLS
Hi Everyone -

I have a classical E&M physics problem that I've been tearing my hair out over. It relates to how ferromagnetic materials boost the field strength of a non-uniform magnetic field. My takeaway from college physics class was that (assuming there's no saturation in the material) the field inside a magnetic material is boosted linearly by a multiplicative constant. So if the field vector at any point in free space p is B(p), if that point in space is enclosed within a magnetic material, the field vector will be αB(p), where α is the relative permeability of the material. But based on some measurements I did, this doesn't appear that my takeaway was correct. It appears instead that there's some sort of "spatial averaging" going on inside the magnetic material, leaving me totally confused. Please see attached for a detailed description of my problem, with images, etc.

Can anyone explain what's going on here? Thanks in advance.

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GaryLS said:
Hi Everyone -

I have a classical E&M physics problem that I've been tearing my hair out over. It relates to how ferromagnetic materials boost the field strength of a non-uniform magnetic field. My takeaway from college physics class was that (assuming there's no saturation in the material) the field inside a magnetic material is boosted linearly by a multiplicative constant. So if the field vector at any point in free space p is B(p), if that point in space is enclosed within a magnetic material, the field vector will be αB(p), where α is the relative permeability of the material. But based on some measurements I did, this doesn't appear that my takeaway was correct. It appears instead that there's some sort of "spatial averaging" going on inside the magnetic material, leaving me totally confused. Please see attached for a detailed description of my problem, with images, etc.

Can anyone explain what's going on here? Thanks in advance.

In your simulation you use an arbitrary increase by a factor of 10 for the induced field within the ferrite core. Have you tried looking up the relative permeability of ferrite (it is more like 640)? Your approach of linear amplification of the induced field within the ferrite does not deal with continuity of the fields and derivatives of the fields at the boundaries of the ferrite material. Any solution of Maxwells equations has to include the behaviour at the boundaries between materials. This will modify the induced field distribution inside the inner perimeter of the ferrite material, within the ferrite material and external to the outer perimeter of the ferrite. The finite length of your ferrite will introduce similar boundary conditions at the axial endpoints as well. What does your experimental measurement suggest is happening? What conclusion can you therefore draw about the your simple linear amplification model of the field within the ferrite?

## 1. What is "spatial averaging" in the context of ferromagnetic materials?

Spatial averaging refers to the process of taking an average of the magnetic properties of a material over a given area or volume. This is often done to account for microscopic variations in the magnetic behavior of a material and to obtain a more accurate representation of its overall properties.

## 2. How is spatial averaging different from other types of averaging?

Spatial averaging is specific to ferromagnetic materials and takes into account the spatial distribution of magnetic properties within the material. This is different from other types of averaging, such as temporal averaging, which considers variations over time, or frequency averaging, which considers variations over different frequencies.

## 3. Why is spatial averaging important in the study of ferromagnetic materials?

Ferromagnetic materials often exhibit microscopic variations in their magnetic properties, which can affect their overall behavior. By using spatial averaging, scientists are able to obtain a more accurate understanding of the material's properties and how it will behave in different situations.

## 4. What techniques are used for spatial averaging in the study of ferromagnetic materials?

There are several techniques that can be used for spatial averaging, such as magnetometry, magnetic force microscopy, and magnetic resonance imaging. These techniques allow scientists to map out the magnetic properties of a material over a given area or volume, which can then be averaged to obtain a representative value.

## 5. Are there any limitations to using spatial averaging in the study of ferromagnetic materials?

While spatial averaging can provide a more accurate representation of a material's magnetic properties, it is important to note that it is still a simplified approach and may not fully capture the complexity of the material's behavior. Additionally, the accuracy of spatial averaging may be limited by the resolution of the measurement techniques used.

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