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According to Steinmetz hysteresis law, hysteresis loss in a material is proportional to

$B$

$B^{1.2}$

$B^{1.6}$

$B^2$

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalElectrical Materials

Option C

$B^{1.6}$

Quick Summary:

According to the Steinmetz hysteresis law, the hysteresis loss ( $W_h$ ) in a ferromagnetic material is empirically proportional to the 1.6th power of the maximum flux density ( $B_{max}$ ) · This relationship is expressed as $W_h = \eta B_{max}^{1.6} f V$ , where $\eta$ is the Steinmetz hysteresis coefficient.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$W_h = \eta B_{max}^{1.6} f V$ — Steinmetz hysteresis loss equation, where $W_h$ is energy loss (Joules), $\eta$ is the material constant, $f$ is frequency, and $V$ is volume.

⚙️ Working Principle

Hysteresis loss occurs due to the energy consumed in rotating and aligning magnetic dipoles within the material as the magnetizing field reverses periodically · Each reversal requires overcoming internal molecular friction, leading to a loop in the B-H curve where the area represents the energy dissipated as heat per cycle · Because this energy loss depends on the volume, frequency of reversal, and the peak induction level, the Steinmetz empirical formula accurately predicts this energy dissipation for technical applications.

📌 Key Points

▸
Hysteresis loss depends on the magnetic properties of the material (hysteresis coefficient $\eta$ ).
▸
Losses are directly proportional to the frequency of the alternating magnetic field.
▸
The 1.6 exponent is an empirical value valid for most silicon steel grades used in transformers.
▸
Higher flux density leads to larger hysteresis loops, resulting in increased heat generation.

✅ Advantages

▸
Allows engineers to estimate heating in transformer cores accurately.
▸
Helps in selecting core materials with low $\eta$ values to improve efficiency.

❌ Disadvantages / Limitations

▸
The law is empirical and may vary slightly for non-standard magnetic materials or high flux saturation regions.
▸
Does not account for eddy current losses separately.

🛠️ Applications / Uses

▸
Transformer core design
▸
Electric machine design (Motors/Generators)
▸
Inductor and Choke design

📄 Additional Information

▸
Steinmetz hysteresis exponent typically ranges between 1.5 and 2.5 depending on the material, but 1.6 is the standard accepted value for common engineering calculations.
▸
Options A, B, and D are incorrect as they do not match the empirically derived Steinmetz relationship.

📊 Diagram / Illustration

✅

C is correct — The Steinmetz hysteresis law defines hysteresis loss as being proportional to the 1.6th power of the maximum flux density ( $B^{1.6}$ ).

Core Concepts Used

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Magnetic Hysteresis Steinmetz Empirical Law Ferromagnetic material losses

💡 EXAM TIP

In competitive exams, always remember that hysteresis loss is proportional to frequency ( $f$ ) and $B^{1.6}$ , whereas eddy current loss is proportional to $f^2$ and $B^2$ .

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