Ferromagnetism – trend of relative permeability with increasing flux density In a ferromagnetic specimen, as the flux density increases from zero up to about 2.5 T, how does the relative permeability µr typically vary?

Introduction:
Relative permeability µr characterizes how easily a material magnetizes under an applied field. In ferromagnetic materials, domain processes dominate at low to moderate fields, producing a nonlinear relationship between B and H. Knowing the typical trend of µr with B helps prevent saturation and optimize magnetic circuit design.

Given Data / Assumptions:

• Ferromagnetic material subjected to a quasi-static magnetization curve.
• Flux density B ramps from 0 toward high values (e.g., near 2.5 T).
• No severe hysteresis loop considerations for the qualitative trend.

Concept / Approach:

At very low fields, domain wall motion is easy and µr rises rapidly. As B increases toward the knee of the magnetization curve, µr reaches a maximum. Beyond the knee, many domains are aligned, incremental permeability drops, and µr decreases as the material approaches saturation. This yields the characteristic “first increase, then decrease” behavior with rising B.

Step-by-Step Solution:

Verification / Alternative check:

Manufacturer B–H curves for electrical steels clearly show initial permeability increase followed by decline beyond the knee, confirming the trend.

Why Other Options Are Wrong:

Monotonic increase or decrease ignores domain behavior and saturation; constant µr would imply linear materials, not ferromagnets.

Common Pitfalls:

Assuming a fixed µr for all operating points; neglecting the difference between initial, maximum, and incremental permeability.

Final Answer:

first increase then decrease