According to Steinmetz hysteresis law, hysteresis loss in a material is proportional to
A
$B$
B
$B^{1.2}$
C
$B^{1.6}$
D
$B^2$

Question

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

Examoogle · Accepted Answer

$B^{1.6}$

Explanation: 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.

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 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.

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

Additional Info: 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.

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

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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