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Steinmetz Decoded

Steinmetz Hysteresis Law

Original Form To Preserve

Section titled “Original Form To Preserve”

The working historical form is:

W=ηB1.6W = \eta B^{1.6}

where W is the energy lost per cycle per unit volume in the historical unit frame, eta is the coefficient of hysteresis, and B is magnetic density or magnetic induction.

The power form multiplies the per-cycle loss by frequency:

P=fηB1.6P = f\eta B^{1.6}

Source Meaning

Section titled “Source Meaning”

The OCR candidate in Alternating Current Phenomena states that hysteresis loss is, with engineering exactness, proportional to the 1.6 power of magnetic induction. The Theoretical Elements OCR gives the same law in a teaching context and identifies eta as the coefficient of hysteresis. Engineering Mathematics then treats the 1.6 power as an empirical curve law rather than a deduction from first principles.

Modern Equivalent

Section titled “Modern Equivalent”

Modern magnetic-core loss models often separate hysteresis loss, eddy-current loss, and excess loss. A simplified Steinmetz-style form is still recognizable:

Ph=khfBmax⁡nP_h = k_h f B_{\max}^{n}

The exponent n is material- and model-dependent in modern use. The historically important Steinmetz value is n = 1.6.

Interactive Translation

Section titled “Interactive Translation”

Use the Hysteresis Loop and Steinmetz Loss tool to vary B, f, eta, and n. The tool keeps the coefficient in adjustable units until the archive completes source-unit verification.

Physical Meaning

The law says that increasing magnetic density raises hysteresis loss faster than linearly. This is why magnetic material, flux density, frequency, and saturation margin become practical design questions rather than decorative theory.

Historical Note

Steinmetz’s law is especially important because it turned magnetic hysteresis into an engineering calculation. It let designers estimate iron loss instead of treating magnetic material lag as a vague qualitative defect.

Interpretive Reading

Interpretive only: field-centered readers may treat hysteresis as field lag or memory. The source-grounded claim is narrower: Steinmetz models hysteresis as a measurable energy loss tied to cyclic magnetic induction.

Still To Verify

Section titled “Still To Verify”
  • Exact source typography for eta, B, W, and P.
  • Historical unit conventions in each source.
  • Whether each edition uses magnetic density, magnetic induction, or another phrase in the immediate formula context.
  • How Steinmetz separates hysteresis loss from eddy-current and saturation losses in the surrounding passages.