Magnetic materials: What is the typical relative permeability (μ_r) for common transformer iron (silicon steel used in power transformers)?

Introduction / Context:
Transformer cores are made from ferromagnetic materials (often silicon steel) chosen for their high magnetic permeability. Knowing a realistic order of magnitude for relative permeability helps students estimate magnetizing current, core size, and inductance, and avoids confusing absolute permeability with the dimensionless relative permeability μ_r used in most transformer discussions.

Given Data / Assumptions:

• The question refers to typical transformer iron used in power-frequency transformers (not exotic alloys).
• Permeability is the relative permeability μ_r (dimensionless), not absolute μ in H/m.
• We assume unsaturated operation near the linear region of the B–H curve at 50/60 Hz.

Concept / Approach:
Relative permeability μ_r = μ / μ0 indicates how many times more a material supports magnetic flux compared with free space. Transformer-grade steels generally have μ_r from a few hundred to a few thousand depending on lamination, silicon content, stress, and flux density. Values around 1,000–5,000 are common, while specialized alloys (e.g., permalloy) can be much higher. A value of about 1,500 is a widely cited nominal for plain transformer iron under typical conditions.

Step-by-Step Solution:

Verification / Alternative check:
Engineering handbooks and manufacturer datasheets for silicon-steel laminations show μ_r varying with B and frequency; nominal catalog points often lie near 1,000–2,000 for practical, linear operation, supporting the selection of 1,500 as a typical figure.

Why Other Options Are Wrong:

• 50: Characteristic of weakly magnetic materials, not transformer iron.
• 450: Possible but on the low side; not representative as a general “typical” value.
• 5,500: More representative of specialty high-permeability alloys, not standard transformer lamination steel.

Common Pitfalls:
Confusing relative and absolute permeability or quoting values measured at very low flux density that do not reflect typical operating points.

Final Answer:
1,500