Why is hysteresis loss proportional to area hysteresis loop ?

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Discussion Overview

The discussion revolves around the relationship between hysteresis loss and the area of the hysteresis loop, particularly in the context of ferromagnetism. Participants explore the reasons behind hysteresis loss causing heat and its proportionality to the area of the loop, delving into both theoretical and conceptual aspects.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions the specifics of the hysteresis loop, asking for clarification on the axes and dimensions involved.
  • Another participant identifies the horizontal axis as H (magnetic field strength) and the vertical axis as B (magnetic flux density).
  • A further contribution explains that ferromagnetism involves an energy gap between magnetized and unmagnetized states, suggesting that work is required to change magnetization, which is represented by the area under the hysteresis curve, expressed mathematically as the integral of H and B.

Areas of Agreement / Disagreement

Participants have not reached a consensus; there are clarifications on the axes of the hysteresis loop, but the broader implications of hysteresis loss and its relationship to heat remain open for further discussion.

Contextual Notes

Some assumptions about the nature of the energy gap and the conditions under which ferromagnetism occurs are not fully explored, and the mathematical representation of the area under the curve is presented without detailed derivation.

fxdung
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Why does hysteresis loss cause heat and why the heat proportional the area of hysteresis loop?
 
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Perhaps you can tell us what loop you are talking about: what's on the horizontal axis and what's on the vertical axis ? So what's the dimension of the area ?
 
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The horizontal axis is H and the vertical axis is B
 
Ferromagnetism occurs when it is energetically favorable that the spins of the electrons in the material are ordered in one direction and there's an "energy gap" between this magnetized state and the unmagnetized state. The microscopic reason that this happens in some few materials is quantum-mechanical. On the macroscopic level it's sufficient to know that this energy argument holds. This, however implies that to change the magnetization you need to do work to redirect the spins, and the change of energy is given by ##\int \mathrm{d} H B##, i.e., the area under the hysteresis curve.
 
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