Magnetic–Electric Analogy – Permeability Correspondence In electromagnetic–electrical analogies, magnetic permeability μ is most closely analogous to which electrical property?

Introduction / Context:Field analogies help engineers intuit equations by mapping magnetic quantities to electrical counterparts. In simple linear media, relationships B = μ H and J = σ E have similar forms, allowing permeability μ to be compared with electrical conductivity σ in terms of how strongly the medium responds to an applied field.

Given Data / Assumptions:

• Linear, isotropic media for both electric and magnetic cases.
• Constitutive relations: B = μ H; J = σ E.
• Analogy focuses on proportionality constants governing response strength.

Concept / Approach:

The medium “gain” from field to flux/current is set by μ (magnetic) and σ (electric). Higher μ yields more magnetic flux density per unit magnetic field, just as higher σ yields more current density per unit electric field. By this mapping, μ ↔ σ and, correspondingly, magnetic reluctivity (1/μ) ↔ electrical resistivity (ρ = 1/σ).

Step-by-Step Solution:

Verification / Alternative check:

In magnetic circuit analogies: Φ = F / ℜ with ℜ ∝ 1/μ mirrors Ohm’s law I = V / R with R ∝ 1/σ, again mapping μ to σ.

Why Other Options Are Wrong:

• Resistivity corresponds to magnetic reluctivity (inverse of μ), not μ itself.
• Retentivity and coercivity are hysteresis characteristics without a direct linear analogue to σ.

Common Pitfalls:

Mixing up direct and inverse analogies; conflating hysteresis properties with constitutive constants.

Final Answer:

Conductivity