magnetic permeability
Enable an agent to interpret, compare and apply magnetic permeability while checking that its definition, material state and measurement conditions support the intended magnetic-field calculation.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
recalled by Codex without web access - no source was read
Researched by: Codex
Purpose and description
Enable an agent to interpret, compare and apply magnetic permeability while checking that its definition, material state and measurement conditions support the intended magnetic-field calculation.
Magnetic permeability characterizes the relationship between magnetic flux density B and magnetic field strength H in a medium, expressed as B = μH for a linear isotropic medium, with more general descriptions needed for anisotropy, nonlinearity, hysteresis and frequency dependence.
It can be Classify a reported permeability by its defining operation, normalization and representation.; Convert between absolute and relative permeability using a declared μ0 reference while preserving conditions and uncertainty.; Select a permeability value, curve or tensor compatible with an intended operating point and field model.; Identify when two reported values are comparable and flag missing conditions that prevent comparison.; Request measurements or constitutive data needed when a scalar constant cannot support the intended calculation.; Assess whether an apparent or effective value can transfer from its measured specimen to another geometry..
Distinguishing features
A permeability relates B to H; susceptibility instead relates magnetization M to H, with conversion requiring a stated convention and constitutive regime.
Absolute permeability has SI units of henries per metre; relative permeability is dimensionless and normalizes the corresponding permeability by vacuum permeability.
Permeability characterizes a response relationship rather than the instantaneous magnitude of B, H or M.
A value obtained as B/H is a secant quantity and generally differs from the local slope dB/dH in a nonlinear or hysteretic material.
A scalar material constant is sufficient only under appropriate assumptions; directional, frequency-dependent or history-dependent response requires additional representation and conditions.
Scope
+ Definitions and distinctions among absolute, relative, secant, differential, initial and incremental permeability
+ Scalar, tensor and complex representations of magnetic response
+ Dependence on field strength, frequency, temperature, direction and magnetic history
+ Measurement, extraction, uncertainty and applicability of reported permeability
+ Distinction between intrinsic material response and effective or apparent permeability
- Magnetic susceptibility as an independently modelled response quantity
- Magnetization, magnetic flux density and magnetic field strength as separate quantities
- Complete hysteresis-loop and magnetic-loss models
- Electrical permittivity and conductivity
- Design and operation of magnets, inductors, transformers and magnetic circuits
- Material composition and manufacturing processes beyond their effects on permeability
Characteristics
- Permeability definition
- absolute or relative; secant, differential, initial, incremental, amplitude or explicitly defined alternative Numerically similar values can describe different response operations and cannot be substituted without checking their definitions.
- Absolute permeability
- H/m, equivalently N/A²; scalar, complex scalar or tensor components Provides the dimensional constitutive coefficient required by a compatible SI field model.
- Relative permeability
- dimensionless; corresponding absolute permeability divided by μ0 Supports normalized comparison while retaining the same operating conditions and response definition.
- Operating field and excitation
- H bias and amplitude in A/m; B bias and amplitude in T; frequency in Hz; waveform Bias, excitation amplitude and frequency determine which local or cycle-dependent response is being described.
- Material condition
- temperature in K; stress in Pa where relevant; magnetic, thermal and processing history Permeability can change when the material state changes even if composition is unchanged.
- Directional representation
- isotropic scalar, diagonal tensor or full tensor with coordinate basis Determines whether B and H may be treated as parallel and how values transform between orientations.
- Complex-response convention
- phasor time convention; real and imaginary parts; component ordering The sign and interpretation of an imaginary component depend on the adopted convention.
- Response attribution
- vacuum, constituent material, specimen, composite or homogenized structure Separates a material response from values that incorporate geometry, interfaces or an extraction model.
- Validity and uncertainty
- uncertainty or interval with coverage basis; supported ranges of field, frequency, temperature and direction Allows an agent to assess whether a value is sufficiently supported for comparison or prediction.
Also called
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 6 bundles · 11 layers · 19 findings · 30 questions.
Constitutive meaning Establishes exactly what relationship a reported permeability represents.
The word permeability alone does not identify a unique operation on magnetic response data.
Field relationship
Identifies the fields, constitutive assumptions and normalization.
B-H relationship
Record whether permeability represents a linear relation B = μH, a local perturbation relation or another explicitly defined operation; include offsets or history dependence when required.
- What equation defines this permeability, and does it relate total fields or changes about an operating point? definition
- Would remanence, nonlinearity or hysteresis make the proposed B = μH interpretation inadequate? boundary
Normalization and neighbouring quantities
Separates absolute permeability, relative permeability and susceptibility.
Normalization convention
Record units and the reference used for μr = μ/μ0. Relations to susceptibility must use compatible SI definitions, operating conditions and scalar or tensor representations.
- Is the reported quantity absolute or relative permeability, and which unit system and μ0 reference are used? definition
- If susceptibility is used to derive permeability, are its response definition and representation compatible with the conversion? boundary
Operating point and history Locates permeability within the material's field-dependent and history-dependent response.
A permeability value can become misleading when separated from its bias, excitation amplitude or magnetic preparation.
Slope and amplitude
Distinguishes ratios, local derivatives and finite-excursion measures.
Response operation
Record whether the value is a secant ratio, local differential slope, initial response or finite-excursion measure, rather than inferring the operation from the label.
- Is this value calculated from B/H, dB/dH, ΔB/ΔH or an amplitude-based procedure? definition
- What bias point, excursion amplitude and curve segment were used? measurement
Magnetic preparation
Captures the history and material conditions that establish the measured response.
State-qualified permeability
Associate the value with its demagnetization or magnetization procedure, hysteresis branch, temperature and other relevant conditions.
- What magnetic preparation and field trajectory produced the state in which permeability was evaluated? provenance
- Which temperature, stress or processing conditions must be preserved for this value to remain applicable? boundary
Dynamic and directional response Represents response that cannot be expressed adequately by one real scalar.
Frequency dependence, phase lag and anisotropy change both the mathematical representation and permissible uses of permeability.
Frequency and phase
Qualifies dynamic permeability by excitation and complex-number conventions.
Complex permeability
Record frequency, waveform, amplitude and phasor convention when permeability describes harmonic response. Do not interpret the imaginary component without the convention and extraction assumptions.
- At what frequencies and excitation amplitudes were the real and imaginary components obtained? measurement
- Which time dependence and complex-permeability sign convention define the reported components? definition
Anisotropy and basis
Records orientation and coupling between field components.
Tensor permeability
Identify the coordinate basis, material orientation and bias conditions for tensor components; justify any reduction to a scalar or diagonal representation.
- Which axes and bias direction define the reported components, and are off-diagonal terms relevant? definition
- What evidence supports using a scalar permeability for the intended field orientation? boundary
Measurement and attribution Connects permeability values to measurements, specimens and extraction assumptions.
Measured magnetic response can include geometry and electromagnetic effects that prevent direct attribution to an intrinsic material property.
Measurement chain
Captures the observations and corrections from which permeability was obtained.
Traceable extraction
Record the method, specimen dimensions, calibration, field estimation and uncertainty supporting a reported value or curve.
- Which measured observables and extraction equation produced the permeability? provenance
- How were calibration, dimensional uncertainty and relevant parasitic effects accounted for? measurement
Intrinsic versus effective
Determines which physical system owns the reported response.
Geometry and homogenization
Distinguish permeability attributed to a material from apparent specimen response or an effective composite or structural response, including demagnetizing-field and homogenization assumptions.
- Does the reported H denote internal material field or externally applied field, and how were demagnetizing effects treated? measurement
- Does this permeability belong to a constituent material, a specific specimen or a homogenized structure? boundary
- What geometry or scale assumptions must hold before transferring it to another system? action
Applicability and agent decisions Determines whether available permeability evidence supports an intended comparison or calculation.
An agent needs explicit criteria for selecting data and recognizing when additional response information is required.
Validity envelope
Defines the supported operating region and limits of interpolation or extrapolation.
Supported operating region
Associate each value, curve or tensor with supported field, frequency, temperature and orientation ranges and its uncertainty.
- Does the intended operating condition lie inside the region supported by measurements or a validated constitutive model? boundary
- What further data are needed if operation approaches saturation, resonance or another unsupported response regime? action
Comparison and model selection
Matches the permeability representation to the decision being made.
Compatible use
Compare values only after matching definitions and conditions, and choose a constant, curve, complex response, tensor or richer constitutive model according to the intended calculation.
- Do the candidate values use compatible response definitions, frequencies, bias conditions, orientations and material states? boundary
- Can the intended calculation use the available permeability representation, or does it require fuller nonlinear or hysteretic response data? action
Evidence and external alignment What the world already says about this thing, gathered so the model can be checked against it.
A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.
Reported evidence
Findings from the breadth pass, kept separate from the structural claims.
Check these first
Recalled without web access and unsourced; every item is a lead to verify.
- This is recalled knowledge, not source-verified research; check the applicable IEC 60404 part and edition for a particular material and measurement method.
- A material permeability value needs its field amplitude, bias, frequency, temperature, specimen geometry and magnetic history specified; anisotropic response may require a tensor.
- In the revised SI, μ₀ is experimentally determined rather than fixed exactly at 4π × 10⁻⁷ H/m; check a current CODATA adjustment if precision matters.
- Which of these check these first hold for the sense of magnetic permeability this model covers, and on what evidence? provenance
Kinds and varieties
Recalled without web access and unsourced; every item is a lead to verify.
- Absolute permeability
- Relative permeability
- Initial permeability
- Differential or incremental permeability
- Effective permeability
- Complex permeability
- Which of these kinds and varieties hold for the sense of magnetic permeability this model covers, and on what evidence? provenance
Identifiers and schemes
Recalled without web access and unsourced; every item is a lead to verify.
- Physical quantity symbols - μ, μ₀, μᵣ - Common symbols for absolute permeability, vacuum permeability and relative permeability respectively; these are quantity symbols, not unique registry identifiers.
- Which of these identifiers and schemes hold for the sense of magnetic permeability this model covers, and on what evidence? provenance
Standards and regulation
Recalled without web access and unsourced; every item is a lead to verify.
- IEC 60404 series, Magnetic materials, issued by the International Electrotechnical Commission, covers magnetic material characterization and measurement methods.
- The SI Brochure, issued by the International Bureau of Weights and Measures, establishes the SI framework in which permeability is expressed in henries per metre.
- Which of these standards and regulation hold for the sense of magnetic permeability this model covers, and on what evidence? provenance
Real-world use
Recalled without web access and unsourced; every item is a lead to verify.
- Selecting magnetic core materials for transformers, inductors and electromagnets.
- Calculating magnetic fields and magnetic circuit reluctance.
- Designing magnetic shielding.
- Characterizing materials through permeability measurements and magnetic nondestructive testing.
- Modelling frequency-dependent magnetic response and losses in electromagnetic components.
- Which of these real-world use hold for the sense of magnetic permeability this model covers, and on what evidence? provenance
Typical measurements
Recalled without web access and unsourced; every item is a lead to verify.
- Vacuum permeability μ₀ - Approximately 1.25663706 × 10⁻⁶; a reference constant rather than a material range. - H/m
- Relative permeability μᵣ = μ/μ₀ - Exactly 1 for vacuum by definition; near 1 for weakly magnetic materials; soft magnetic materials can exhibit values from hundreds to hundreds of thousands under specified conditions. - dimensionless
- Differential permeability dB/dH - No universal range; depends on material, operating point and magnetic history. - H/m
- Which of these typical measurements hold for the sense of magnetic permeability this model covers, and on what evidence? provenance
Failure modes and hazards
Recalled without web access and unsourced; every item is a lead to verify.
- Treating permeability as constant near magnetic saturation can substantially mispredict inductance and current.
- Ignoring hysteresis and magnetic history can make a single reported permeability value misleading.
- Using low-frequency permeability at high frequencies can mispredict component response, losses and heating.
- Confusing intrinsic material permeability with effective permeability of a gapped or shaped component can produce design errors.
- Ignoring temperature, mechanical stress or directional dependence can invalidate measured or tabulated values.
- Which of these failure modes and hazards hold for the sense of magnetic permeability this model covers, and on what evidence? provenance
Regional variation
Recalled without web access and unsourced; every item is a lead to verify.
- SI and Gaussian-CGS conventions differ in their electromagnetic equations and treatment of permeability; values and formulas require explicit unit-system identification.
- Which of these regional variation hold for the sense of magnetic permeability this model covers, and on what evidence? provenance
Neighbouring kinds and how to tell them apart
Recalled without web access and unsourced; every item is a lead to verify.
- Magnetic susceptibility - Susceptibility relates magnetization M to H; permeability relates B to H. For a linear isotropic medium in SI, μᵣ = 1 + χ.
- Magnetic flux density - B is a magnetic field quantity measured in teslas; permeability describes the constitutive relationship involving B and H.
- Magnetic field strength - H is a magnetic field quantity measured in amperes per metre; permeability relates it to magnetic flux density under specified conditions.
- Magnetic reluctivity - Reluctivity is the reciprocal of scalar permeability, or the inverse permeability tensor where applicable.
- Magnetic permeance - Permeance describes a magnetic circuit or component and depends on geometry as well as permeability.
- Electrical permittivity - Permittivity relates electric displacement to electric field; permeability concerns magnetic response.
- Which of these neighbouring kinds and how to tell them apart hold for the sense of magnetic permeability this model covers, and on what evidence? provenance
What the second pass must settle
- Which authoritative references and measurement standards should anchor the publication's definitions of initial, incremental and amplitude permeability, including differences between their conventions?
- How broadly should this entry cover effective permeability of metamaterials and spatially dispersive media, where a local constitutive coefficient may be inadequate?
- What minimum measurement metadata should be required for different specimen types before an agent treats a reported permeability as transferable?
- Which neighbouring Vercy models already own susceptibility, magnetization, hysteresis and magnetic material state, and where should this entry link to them?
- How should the publication represent superconducting screening and other cases where an apparent permeability depends strongly on geometry and the field model?