In ferromagnetic materials, the observed time-dependent lag of magnetic flux density B relative to magnetizing force H under alternating excitation is known as what phenomenon?

Introduction / Context:
When ferromagnetic materials are subjected to alternating magnetizing force, the relationship between B and H is not single-valued. Instead, a loop forms in the B–H plane because B lags H. This behavior is central to understanding core losses and dynamic magnetics in transformers, inductors, and motors.

Given Data / Assumptions:

• Alternating magnetizing force H(t).
• Ferromagnetic core material with domain dynamics.
• Quasi-periodic steady state.

Concept / Approach:
The lag between B and H is called hysteresis. The B–H trajectory forms a closed loop over a cycle; the enclosed area equals energy lost per unit volume per cycle (hysteresis loss). Coercivity (the field required to reduce B to zero after saturation) and remanence (residual B when H returns to zero) are parameters describing hysteresis behavior.

Step-by-Step Explanation:
Apply alternating H → domains rotate and switch with delay.B does not instantaneously follow H → phase and state-dependent lag arises.Plot B vs H over a cycle → a loop appears; its area corresponds to hysteresis energy loss.This phenomenon is termed hysteresis.

Verification / Alternative check:
Measuring core loss vs frequency shows a component roughly proportional to frequency (hysteresis) and another to frequency squared (eddy current), confirming distinct mechanisms.

Why Other Options Are Wrong:

• Eddy current: Circulating currents causing I^2R losses; not the B–H lag itself.
• Saturation: The knee where B increases slowly with H; not a lag term.
• Coercivity: A specific hysteresis parameter, not the entire lag phenomenon.
• Paramagnetism: Weak, linear magnetization without hysteresis loop.

Common Pitfalls:

• Equating all core losses to hysteresis; eddy currents also contribute significantly.
• Confusing coercivity or remanence (points on the loop) with the loop phenomenon itself.

Final Answer:
hysteresis