Magnetic materials – variation of relative permeability with flux density An iron specimen has relative permeability µr = 1000 at flux density B = 0.30 T. When B increases to 0.35 T, how will µr typically change?

Introduction:
The B–H characteristics of ferromagnetic materials are nonlinear. Relative permeability µr varies with operating point and generally peaks near the knee of the magnetization curve before declining as the material moves toward saturation. Designers must understand this trend to avoid excessive magnetizing current and core losses.

Given Data / Assumptions:

• Material: iron specimen (ferromagnet).
• Initial operating point: B = 0.30 T with µr = 1000.
• New operating point: B = 0.35 T (higher flux density).

Concept / Approach:

As B increases beyond the region of maximum incremental permeability, domains become increasingly aligned; the remaining unaligned domains contribute less to further increases in B per unit H, reducing incremental µ. Therefore, moving to a higher B (0.35 T) from 0.30 T typically results in a decrease in µr, unless the initial point was far below the knee (which is uncommon for iron near these B values).

Step-by-Step Solution:

Verification / Alternative check:

Typical catalog B–H curves for electrical steels show µr peaking at modest B (often 0.1–0.3 T), then declining toward higher B, confirming the qualitative change.

Why Other Options Are Wrong:

Constant or increased µr contradicts standard ferromagnetic behaviour near saturation; “may be more or less” is non-committal and usually untrue for this B range; zero is impossible for a ferromagnet in this region.

Common Pitfalls:

Assuming µr is constant like in linear dielectrics; ignoring that engineering “µr” quoted is operating-point dependent.

Final Answer:

will be less than 1000