Electromagnetism history – who first related hysteresis loss to maximum flux density? Identify the scientist who first established the empirical relationship between hysteresis loss in ferromagnetic materials and the maximum flux density reached during the magnetization cycle.

Introduction:
Hysteresis loss is the energy dissipated in a ferromagnetic material during a complete cycle of magnetization. This loss depends on the shape and area of the B–H loop and is particularly important in transformers and rotating machines. The first widely used empirical relation connecting hysteresis loss to the maximum flux density was credited to Charles Proteus Steinmetz, a pioneer in electrical engineering at the turn of the 20th century.

Given Data / Assumptions:

• We are discussing ferromagnetic core losses under periodic excitation.
• Maximum flux density B_max is the peak flux density in a cycle.
• Classical empirical form: Ph ∝ B_max^n * f, with n typically between 1.5 and 2.5 for many steels.

Concept / Approach:

Steinmetz introduced an empirical law to estimate hysteresis loss from readily known quantities like frequency and maximum flux density, enabling engineers to size magnetic cores and predict heating. Although later refinements separated eddy-current and anomalous losses, the “Steinmetz equation” remains foundational in magnetic design practice and education.

Step-by-Step Solution:

Verification / Alternative check:

Modern magnetic core loss models still cite Steinmetz’s original formulation or generalized versions (e.g., improved/modified Steinmetz equations) as a starting point, confirming the attribution.

Why Other Options Are Wrong:

Kirchhoff is known for circuit current/voltage laws; Laplace for fields/forces in magnetostatics; Ampere for magnetomotive force and currents; Maxwell for electromagnetic field theory—none originated the hysteresis–B_max empirical loss law.

Common Pitfalls:

Confusing eddy-current loss (depends on B_max^2, thickness, resistivity) with hysteresis loss; attributing the empirical relation to Maxwell or Kirchhoff due to their fame rather than historical accuracy.

Final Answer:

C. Steinmetz