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:
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:
Final Answer:
Proportional to B_max^1.6
Discussion & Comments