Haow is magnetic permeability measured?

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Magnetic permeability is measured by ensuring the sample is in a configuration that minimizes stray fields, allowing for accurate measurements of H and B. The standard approach involves using advantageous geometries to achieve consistent results independent of the material's shape. A common method is to close the magnetic circuit to eliminate stray fields, ensuring H equals H0. Concerns about using samples in circuits with larger air gaps are addressed by recognizing that measured permeability still provides valuable information despite potential variations. Understanding these principles clarifies the relationship between magnetic fields and permeability.
Hassan2
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My research is related to magnetism and I'm supposed to have a good understanding of permeability but I'm afraid I don't.

My question is that how is permeability of a mater measured so that it becomes independent of the geometry and configuration?

Thanks.
 
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You just have to measure it for an advantageous geometry. I think your problem is more due to assuming that permeability should link H_0 to B and not H to B, as is standard.
 
You are right. My problem was mainly due to the wrong assumption. But then how can we measure H ? I remember once my professor was explaining that the sample should close a magnetic circuit so that the stray field becomes zero, then we have H=H_{0}. Since then I was wondering if we use the sample in a circuit with larger air gaps, how the measured permeability would be useful. I think now I understand the relation. Thanks a lot.
 
It may be shown from the equations of electromagnetism, by James Clerk Maxwell in the 1860’s, that the speed of light in the vacuum of free space is related to electric permittivity (ϵ) and magnetic permeability (μ) by the equation: c=1/√( μ ϵ ) . This value is a constant for the vacuum of free space and is independent of the motion of the observer. It was this fact, in part, that led Albert Einstein to Special Relativity.
This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...

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