Materials property: What is the (absolute) magnetic permeability of machine steel, expressed in henry per meter (H/m), from the typical reference values below?

Introduction / Context:
Magnetic permeability μ characterizes how a material responds to magnetic fields and is central to inductor/transformer core design. Machine steel is a common ferromagnetic material with a permeability significantly higher than free space μ0 (≈ 1.256 × 10^−6 H/m) but much lower than specialized high-permeability alloys.

Given Data / Assumptions:

• Choices represent absolute permeabilities in H/m.
• Typical machine steel has moderate relative permeability μr on the order of a few hundred.
• Operating in the linear region (unsaturated).

Concept / Approach:
Absolute permeability μ = μ0 * μr. If μr is a few hundred, μ is on the order of 10^−4 to 10^−3 H/m. Among the options, 5.65 × 10^−4 H/m aligns well with a μr around 450, consistent with “machine steel” rather than specialized silicon steel or high-μ alloys.

Step-by-Step Solution:

Verification / Alternative check:
Comparing with reference tables for common steels shows values in this range when unsaturated; much larger values would imply specialized cores (e.g., permalloy) rather than machine steel.

Why Other Options Are Wrong:

• 1.1 × 10^−4: Too low (μr ≈ 87), not typical for machine steel.
• 6.9 × 10^−3 or 8.8 × 10^−3: Too high; such μ implies specialty alloys or measurement at very low flux densities.

Common Pitfalls:
Confusing absolute and relative permeability or assuming a constant μ regardless of flux density; real materials are nonlinear and frequency dependent.

Final Answer:
5.65 × 10^−4