What is the formula to obtain the hysteresis loss devised by Steinmetz?

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Examoogle · Accepted Answer

hysteresis loss = hysteresis coefficient * frequency of magnetization * (maximum flux density)^{Steinmetz coefficient}

Explanation: Steinmetz's hysteresis loss formula states that the power loss due to magnetic hysteresis in a ferromagnetic material is directly proportional to the frequency of magnetization and the maximum flux density raised to the power of the Steinmetz coefficient. The mathematical expression is given by $P_h = \eta f B_{max}^n$, where $\eta$ is the Steinmetz hysteresis coefficient. Working Principle: When a ferromagnetic material is subjected to an alternating magnetic field, the magnetic domains within the material are forced to align and realign with the field. This constant rotation and movement of domains consume energy, which is dissipated as heat within the material. The Steinmetz empirical relation models this energy dissipation per cycle, accounting for the material's specific magnetic properties through the coefficient $\eta$ and the exponent $n$, which typically ranges between 1.6 and 2.5. Key Formulas: $P_h = \eta f B_{max}^n$ — Steinmetz hysteresis loss equation; $P_{total} = P_h + P_e$ — Total iron loss where $P_e$ is eddy current loss Key Points: Hysteresis loss depends on the magnetic material properties (hysteresis coefficient).; It is directly proportional to the operating frequency $f$.; The exponent $n$ (Steinmetz coefficient) is constant for a given range of flux densities.; Hysteresis loss is represented by the area of the B-H loop. Advantages: Provides a simple empirical model for power engineers.; Essential for calculating transformer and motor core losses. Disadvantages: It is an empirical formula, not derived from first principles.; The constant $n$ varies with the material and the range of flux density. Applications: Transformer design and efficiency optimization.; Electrical machine core design.; Magnetic material characterization. Additional Info: Typical value of the Steinmetz exponent 'n' for silicon steel is approximately 1.6.. Option A, B, and D are incorrect as they propose division by frequency or coefficient, which contradicts the established physical proportional relationship. Answer: C is correct — The Steinmetz formula for hysteresis loss is given by the product of the hysteresis coefficient, the frequency of magnetization, and the maximum flux density raised to the power of the Steinmetz coefficient. Exam Tip: Always remember that hysteresis loss is directly proportional to frequency, whereas eddy current loss is proportional to the square of frequency ($f^2$).

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