Hysteresis loss dependence on flux density If B_max is the maximum flux density, how does magnetic hysteresis power loss depend on B_max (for a given material and frequency range using a Steinmetz-type relation)?

Difficulty: Easy

Correct Answer: Proportional to B_max^1.6

Explanation:


Introduction / Context:
Hysteresis loss is associated with irreversible domain wall motion and magnetization reversal in ferromagnetic cores. Engineers often use empirical Steinmetz equations to relate loss to flux density and frequency.



Given Data / Assumptions:

  • Fixed material with given hysteresis characteristics.
  • Frequency in a range where classical Steinmetz parameters apply.
  • We compare dependence on B_max only.



Concept / Approach:
The classical Steinmetz relation expresses hysteresis power loss per unit volume as P_h ∝ f * B_max^n where n is typically around 1.6 for many steels (actual values vary with material and processing). Holding f constant isolates the dependence P_h ∝ B_max^n with n ≈ 1.6.



Step-by-Step Solution:
Adopt Steinmetz form: P_h = k_h * f * B_max^n.With f fixed, P_h ∝ B_max^n.For common lamination steels, n ≈ 1.6 → P_h ∝ B_max^1.6.



Verification / Alternative check:
Manufacturer core-loss curves plotted on log–log axes show slopes near 1.6 in the hysteresis-dominated regime, confirming the exponent.



Why Other Options Are Wrong:
Linear, quadratic, or cubic dependencies do not reflect the empirical hysteresis scaling across typical operating ranges. Independence from B_max contradicts basic magnetization physics.



Common Pitfalls:

  • Confusing hysteresis (≈ B^1.6) with eddy-current loss (∝ B^2 at fixed f).
  • Assuming a universal exponent; it is material-dependent but commonly near 1.6.



Final Answer:
Proportional to B_max^1.6


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