In electromagnetic theory, what is the correct SI unit for magnetic permeability (μ), keeping full dimensional clarity?

Introduction / Context:Understanding units in electromagnetics is essential for interpreting formulas and designing components such as inductors, transformers, and magnetic cores. Magnetic permeability, denoted μ, links magnetic flux density B to magnetic field strength H through B = μ * H. Choosing the correct SI unit ensures dimensional consistency in calculations and specifications.

Given Data / Assumptions:

• Permeability is defined by B = μ * H.
• B (flux density) is measured in tesla, T, which equals Wb/m^2.
• H (magnetic field strength) is measured in ampere-turns per meter (At/m) or equivalently A/m when turns are absorbed into current.

Concept / Approach:The unit of μ follows directly from μ = B / H. Substitute the SI base units for B and H to derive μ’s unit symbolically, then match with the listed options. Keep ampere-turns (At) explicit to align with classic magnetics notation used in many textbooks and data sheets.

Step-by-Step Solution:

Verification / Alternative check:Henry (H) is Wb/A. The widely used engineering unit form for permeability is H/m. Since H = Wb/A and At approximates A when turns = 1, H/m = (Wb/A)/m = Wb/(A·m). With At explicitly shown, Wb/(At·m) is the consistent expression used in many magnetics contexts.

Why Other Options Are Wrong:

• At/Wb: This is the unit of magnetic reluctance, not permeability.
• Wb: Weber alone measures flux, not a material property per length.
• At/m: This is the unit for field strength H, not permeability.

Common Pitfalls:

• Confusing permeability μ with permittivity ε; ε has units F/m, while μ has units H/m.
• Dropping the per-meter factor; permeability is a material property per length dimension.

Final Answer:Wb/At × m