I would like to ask about the mangetic permeability, I have measured the hysteresis loop, its polarization (T) versus magnetic flux density (mT). do we need to convert first polarization to magnetization or we can calculate from the formula mu = J/ H / mu° +1 ...
To get the permeability
you need to take the initial magnetiztion curve and not the loop.
At small fields the curve is reversible and the slope gives intial permeability. Once near saturation one egts the max permeability. In any case a full hysteresis loop is not needed.
To get the permeability
you need to take the initial magnetiztion curve and not the loop.
At small fields the curve is reversible and the slope gives intial permeability. Once near saturation one egts the max permeability. In any case a full hysteresis loop is not needed.
Dear Mudassir Ahmed
It is right, you have to use the initial magnetization curve. Unfortunately, you will not obtain a straight line. Hence, you will obtain the permeability versus the magnetic field. If you need an analytic calculation, this will not help you. You have to use FEM softwares. I have added a short explanation in the attached file.
Best regards.
There are two permeabilities, differential dM/dH and normal delta M/delta H. Differential permeability increases nonlinearly with both applied field and magnetization but normal permeability increases from its reversible value linearly in change in magnetization due to cooperation between magnetic domains. See for example my 2012 publication on Research Gate.
Permeability is NOT the slope between polarisation J and flux density B. Both of these will be very similar at low excitation for soft magnetic materials, so that it is often assumed that B = J.
Permeability, in the understanding of SI units is the slope of the curve of B = f(H) or J=f(H), because by definition B = mu_r * mu_0 * H, where mu_0 is the magnetic constant and mu_r is the relative magnetic permeability (mu_r = 1 for vacuum, by definition).
For engineering-like applications you can derive the amplitude permeability from the B-H loops. For each loop you detect Bpeak and Hpeak and use them to define mu_r as:
mu_r = Bpeak / (Hpeak * mu_0)
This concept is not very precise at high frequencies, because the B-H loops become round and thus Bpeak does not correspond to the same point on the loop as Hpeak. But the concept is good enough for engineering applications, and it can be certainly used as a figure of merit for most studies.
The same applies if J or M is used instead of B.
The first magnetization curve tangent to the curve, so as to under it. Yes designate the initial permeability. The maximum permeability is tangent to the curve but as if over her. Touches on his knee Ewing, at the approach to ferromagnetic saturation.
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