If we have a solenoid electromagnet with an iron core, the magnetic field produced is proportional to the permeability of the iron and the current through the coil. As we increase the current through the coil and the magnetic field increases in strength, wouldn't the permeability of the iron also increase? But this would only happen until the iron core saturates and its permeability reaches a maximum. Is there any way to calculate beforehand at what current the permeability would reach its maximum?
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$\begingroup$ How do you come to the conclusion that permeability should increase? This question is all the more confusing as you seem to know already about saturation. en.wikipedia.org/wiki/Saturation_(magnetic) $\endgroup$– oliverCommented Apr 7, 2022 at 20:11
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The concept of permeability has next to zero applicability for a nonlinear ferromagnet. It is true that the magnetic induction field $B$ and magnetic force $H$ are related but because of hysteresis the relationship between $B$ (or $M$) and $H$ is not even a simple nonlinear function. But if you insist on examining the quantities the ratio $\mu = B/H$ or differential quotient $\tilde \mu = \frac{dB}{dH}$ then your result will depend on the various up or down going branches of the your hysteresis curve. The differential quotient $\frac{dB}{dH}$ is used sometime for analyzing small signals with linearized equations (this is the "next to zero applicability"). The function $B=B(H)$ is monotonically increasing but because of saturation it has an inflection point before saturation and in the limit as $M$ goes to a constant, $\frac{dM}{dH}\to 0$, we have $\mu, \tilde \mu \to \mu_0$ which is its minimum for only in the case of a diamagnet it can be less than $\mu_0$.
