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Suppose I have a ferromagnetic material that is inside a chamber where you can somehow control the magnetic field. The image represents its magnetization in function of its applied magnetic field.

a) By taking that red spot as the starting point of the process, how could we demagnetize that material?

My answer: I would reverse the direction of the magnetic (making it negative instead of positive) field so that we could reach the point where M = 0 in the negative x axis. After that, I would turn off the apparatus responsible for creating the magnetic field in a way that we could get back to the origin point of the graph, making it demagnetized.

b) A scientist claims that if you had only the initial absolute value of the magnetic field inside the chamber, you could precisely determine the whole process of the hysteresis curve. Explain if this makes sense, and what procedures you could do inside the chamber to prove your point.

My answer: Initially, I would think that if you don't have the direction of the applied magnetic field, it's not possible to determine the curve and the material's magnetization process. Unfortunately, i cannot think of anyway to prove my point when inside this fictional chamber.

I'm pretty confident about my first answer, but I'm not quite sure if my way of thinking about the second question is correct. Anyway, could anyone confirm my way of thinking about the a) item and give me some insights about item b)?

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  • $\begingroup$ You might struggle to find people willing to check your answer answer (a) here but (b) is worth a shot. Why do you think the direction of magnetization matters? What different observations would you make if you knew the direction was one thing versus another? $\endgroup$ Jun 14, 2021 at 16:53
  • $\begingroup$ The direction of the alignment of the magnetic dipoles depends on the direction of the magnetic field, doesn't it? $\endgroup$ Jun 14, 2021 at 17:04
  • $\begingroup$ For sure - sorry I meant to ask a more direct question: say you have the absolute value of the magnetic field. What are the possible points on the hysteresis curve on which you can be? What would you expect to happen if you increased vs decreased the magnetic field from that point? Could these different expectations lead you to concrete results while conducting an experiment inside the chamber? $\endgroup$ Jun 14, 2021 at 18:22
  • $\begingroup$ For a given initial value of magnetic field, we have 2 points at the same side of the magnetic field axis. If the field increases, the material tends to saturate. If it decreases until zero, it becomes a permanent magnet. In that sense, increasing and decreasing the field inside the chamber would be enought to determine the whole process. Is that correct? $\endgroup$ Jun 14, 2021 at 19:40

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Accurate modelling of the hysteretic behavior of ferromagnetic materials is a topic of huge commercial interest because of their role in transformers, motors, and generators. There exists a huge body of literature on the topic, e.g. ref. Even if the fields are applied along a single axis, existing models only begin to approximate the behavior.

As an example of the complexity, a given magnetization value may be realized by approaching from a low value by increasing field or from a high value by applying reverse field. Despite having the same net magnetization (including zero magnetization) even at the same applied field, the internal magnetic configuration can be quite different. Accordingly the response to subsequent fields will be different. Hysteresis models have to try to capture this behavior over all possible field histories.

Measurements that try to define the parameters of a hysteresis model are also fraught with difficulties, not only because of the complex role of the field sequence, but also because the measurements are not necessarily very repeatable due to the often chaotic behavior of the internal domain strutures.

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