Magnetic Flux Ontology

# Magnetic Flux Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/electromagnetic-measurements/magnetic-flux-ontology.html

FLOW MagneticFluxOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Electromagnetic Measurements
    -> Magnetic Flux Ontology

  PURPOSE:
    Represent magnetic flux as a measurable scalar surface-integral quantity describing the magnetic flux density passing through an oriented surface, including magnitude, sign, surface orientation, units, dimensional structure, flux linkage, electromagnetic induction, Faraday's law, closed-surface behaviour, measurement methods, uncertainty, and distinctions from magnetic flux density and magnetic field strength.

  ENTITY MagneticFlux {
    TYPE: DerivedElectromagneticQuantity
    SYMBOL: Phi_B
    DIMENSION: M * L^2 * T^-2 * I^-1
    SI_UNIT: weber
    SI_SYMBOL: Wb

    DEFINITION:
      magnetic_flux := surface_integral(MagneticFluxDensity dot DifferentialAreaVector)

    GENERAL_FORM:
      Phi_B = integral_S(B dot dA)

    UNIFORM_PLANAR_FORM:
      Phi_B = B*A*cos(theta)

    PROPERTIES:
      is_scalar_surface_integral_result
      has_sign_relative_to_surface_orientation
      has_value
      has_unit
      has_dimension
      depends_on_surface
      depends_on_surface_orientation
      may_vary_with_time
      may_have_uncertainty
  }

  ENTITY MagneticFluxDensity {
    TYPE: VectorFieldPhysicalQuantity
    SYMBOL: B
    DIMENSION: M * T^-2 * I^-1
    SI_UNIT: tesla
    SI_SYMBOL: T

    RELATION:
      MagneticFlux = surface_integral(B dot dA)
  }

  ENTITY AreaVector {
    TYPE: OrientedGeometricQuantity
    SYMBOL: A_vector
    DIMENSION: L^2

    DEFINITION:
      area_magnitude_times_unit_surface_normal

    RELATION:
      B dot AreaVector -> MagneticFlux
      FOR uniform_planar_field_case
  }

  ENTITY MagneticFieldStrength {
    TYPE: VectorFieldPhysicalQuantity
    SYMBOL: H
    SI_UNIT: ampere_per_metre
    SI_SYMBOL: A/m

    RELATION:
      B = mu*H
      UNDER linear_isotropic_material_context
  }

  ENTITY ElectromotiveForce {
    TYPE: DerivedElectromagneticQuantity
    SYMBOL: emf
    SI_UNIT: volt
    SI_SYMBOL: V

    RELATION:
      emf = -d(MagneticFluxLinkage)/dt
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: weber
      symbol: Wb

      equivalence:
        1 Wb = 1 T*m^2
        1 Wb = 1 V*s
        1 Wb = 1 kg*m^2/(A*s^2)
    }

    COMMON_ALTERNATIVES {
      milliweber
      microweber
      nanoweber
      maxwell
    }

    COMMON_CONVERSION:
      1 Wb = 1e8 maxwell
      1 maxwell = 1e-8 Wb

    CONVERSION_RULE:
      magnetic_flux_value(target_unit)
        = magnetic_flux_value(source_unit)
        * conversion_factor(source_unit, target_unit)
  }

  CLASSIFICATION {
    by surface:
      open_surface_flux
      closed_surface_flux

    by field_geometry:
      uniform_field_flux
      nonuniform_field_flux

    by time:
      static_magnetic_flux
      time_varying_magnetic_flux

    by circuit_context:
      single_turn_flux
      flux_linkage
      leakage_flux
      mutual_flux
  }

  SURFACE_INTEGRAL_MODEL {
    GENERAL:
      Phi_B = integral_S(B dot n_hat dA)

    UNIFORM_FIELD_PLANAR_SURFACE:
      Phi_B = B*A*cos(theta)

    ANGLE:
      theta = angle_between_B_and_surface_normal

    SPECIAL_CASES:
      B_parallel_to_surface_normal:
        abs(Phi_B) = B*A

      B_perpendicular_to_surface_normal:
        Phi_B = 0

    RULE:
      angle_is_with_surface_normal
      NOT directly_with_surface_plane
  }

  ORIENTATION_MODEL {
    surface_normal:
      n_hat

    positive_flux:
      B_component_along_positive_normal > 0

    negative_flux:
      B_component_opposite_positive_normal > 0

    orientation_reversal:
      n_hat -> -n_hat
      causes Phi_B -> -Phi_B

    RULE:
      surface_orientation MUST be preserved
      for signed_flux_and_induction_reasoning
  }

  GAUSS_MAGNETISM_MODEL {
    DIFFERENTIAL_FORM:
      divergence(B) = 0

    CLOSED_SURFACE_FORM:
      closed_surface_integral(B dot dA) = 0

    CONSEQUENCE:
      net_magnetic_flux_through_any_closed_surface = 0
      in_standard_classical_electromagnetism

    RULE:
      zero_net_closed_surface_flux
      DOES_NOT imply B = 0 on_surface
  }

  FARADAY_INDUCTION_MODEL {
    SINGLE_LOOP:
      emf = -dPhi_B/dt
      WHEN Phi_B represents_flux_through_loop_with_consistent_orientation

    FLUX_LINKAGE_FORM:
      emf = -d(lambda_B)/dt

    N_TURN_IDEAL_COIL:
      lambda_B = N*Phi_B
      WHEN each_turn_links_same_flux

    LENZ_SIGN:
      negative_sign encodes_induced_response_opposing_flux_change
      under_consistent_loop_orientation

    RULE:
      orientation_of_loop_and_surface_normal
      MUST be consistent_with_emf_sign_convention
  }

  FLUX_LINKAGE_MODEL {
    ENTITY MagneticFluxLinkage {
      SYMBOL: lambda_B
      SI_UNIT: weber_turn
      COMMON_DIMENSIONAL_EQUIVALENCE: weber
    }

    GENERAL:
      lambda_B = sum(flux_linked_by_each_turn)

    IDEAL_N_TURN:
      lambda_B = N*Phi_B

    INDUCTANCE_RELATION:
      lambda_B = L*I
      UNDER linear_inductor_context

    RULE:
      magnetic_flux_and_flux_linkage
      MUST_NOT be treated_as_identical_when_turn_count_or_linkage_differs
  }

  INDUCTANCE_MODEL {
    SELF_INDUCTANCE:
      L = lambda_B/I
      WHEN I != 0 AND linear_context

    IDEAL_SINGLE_FLUX_N_TURN:
      L = N*Phi_B/I

    INDUCED_VOLTAGE:
      v = -d(lambda_B)/dt
      according_to_orientation_and_passive_sign_convention

    RULE:
      nonlinear_magnetic_materials MAY require differential_or_state_dependent_inductance
  }

  MATERIAL_MODEL {
    LINEAR_ISOTROPIC:
      B = mu*H

    GENERAL:
      B = mu_0*(H + M)

    CONSEQUENCE:
      magnetic_flux depends_on material_response_through_B

    RULE:
      flux_calculation_in_materials SHOULD preserve permeability,
      magnetisation, geometry_and_field_distribution_context
  }

  RELATIONSHIPS {
    MagneticFlux -> SURFACE_INTEGRAL_OF -> MagneticFluxDensity
    MagneticFlux -> HAS_DIMENSION -> M*L^2*T^-2*I^-1
    MagneticFlux -> MEASURED_IN -> Weber
    MagneticFluxDensity -> MEASURED_IN -> Tesla
    MagneticFlux -> DEPENDS_ON -> SurfaceGeometry
    MagneticFlux -> DEPENDS_ON -> SurfaceOrientation
    TimeVaryingMagneticFlux -> INDUCES -> ElectromotiveForce
    MagneticFluxLinkage -> SUMS -> FluxAcrossTurns
    Inductance -> RELATES -> FluxLinkageAndCurrent
    ClosedSurface -> HAS_ZERO_NET -> MagneticFlux
  }

  SEMANTIC_EQUIVALENCE {
    "magnetic flux" ~= Phi_B
    "weber" ~= "Wb"
    "tesla square metre" ~= "T*m^2"
    "volt second" ~= "V*s"

    magnetic_flux != magnetic_flux_density
    magnetic_flux != magnetic_field_strength
    magnetic_flux != magnetic_flux_linkage
    magnetic_flux != electromotive_force
    weber != tesla
  }

  CONSTRAINTS {
    magnetic_flux_is_scalar_surface_integral = true
    magnetic_flux_has_orientation_dependent_sign = true
    dimensional_formula = M*L^2*T^-2*I^-1
    SI_unit = Wb
    flux_requires_defined_surface = true
    signed_flux_requires_surface_orientation = true
    magnetic_flux_and_flux_density_are_not_semantically_equivalent = true
    magnetic_flux_and_flux_linkage_are_not_generally_semantically_equivalent = true
    net_flux_through_closed_surface_is_zero_in_standard_Maxwell_theory = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE_OR_INFERRED:
      MagneticFlux

    COMMON_MEASUREMENT_METHODS:
      fluxmeter
      search_coil
      integrating_voltage_measurement
      Hall_probe_field_mapping_plus_surface_integration
      calibrated_pickup_coil

    INDIRECT_MEASUREMENT:
      integrate_B_over_surface
      integrate_induced_voltage_over_time
      infer_from_flux_linkage_and_turn_count
      infer_from_inductance_and_current_under_applicable_model

    RECORD:
      numerical_value
      unit
      surface_geometry
      surface_area
      surface_orientation
      magnetic_flux_density_field
      time
      coil_turn_count_when_relevant
      loop_orientation
      material_or_core
      instrument
      calibration_state
      integration_interval
      uncertainty

    UNCERTAINTY:
      measured_or_inferred_flux = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF uniform_B_known AND planar_area_known AND angle_to_normal_known
      THEN magnetic_flux = B*area*cos(angle)

    IF B_field_known_over_surface
      THEN magnetic_flux = surface_integral(B dot dA)

    IF surface_orientation_reversed
      THEN signed_magnetic_flux = -previous_signed_magnetic_flux

    IF closed_surface
      THEN net_magnetic_flux = 0
      UNDER standard_classical_Maxwell_context

    IF magnetic_flux_changes_with_time
      THEN induced_emf = -derivative(magnetic_flux, time)
      FOR single_loop_consistent_orientation

    IF N_turns_known AND same_flux_links_each_turn
      THEN magnetic_flux_linkage = N*magnetic_flux

    IF flux_linkage_known_as_function_of_time
      THEN induced_emf = -derivative(flux_linkage, time)

    IF linear_inductance_known AND current_known
      THEN flux_linkage = inductance*current
  }

  GEOMETRY_MODEL {
    REQUIRE:
      surface_definition
      surface_area
      surface_normal
      field_distribution

    nonplanar_surface:
      local_normal_varies_over_surface

    nonuniform_field:
      B varies_over_surface

    RULE:
      B*A*cos(theta) shortcut
      ONLY valid_for_uniform_B_and_planar_or_equivalent_constant_geometry
  }

  TIME_MODEL {
    static_flux:
      dPhi_B/dt = 0

    time_varying_flux:
      dPhi_B/dt != 0

    induced_emf_context:
      requires_flux_change_rate_and_orientation

    RULE:
      constant_nonzero_flux alone
      DOES_NOT induce_emf_by_Faraday_flux_rule
  }

  UNCERTAINTY_MODEL {
    sources:
      magnetic_field_measurement_uncertainty
      surface_area_uncertainty
      orientation_uncertainty
      spatial_sampling
      integration_error
      coil_turn_count
      voltage_measurement_uncertainty
      timing_uncertainty
      calibration_uncertainty
      material_and_geometry_model_uncertainty

    PROPAGATION:
      derived_flux_uncertainty
      <- field_geometry_orientation_and_measurement_uncertainties
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    surface_integral_relationship_confidence: 1.00
    Faraday_relationship_confidence: 1.00
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when surface geometry, orientation,
      B-field distribution, time context, coil linkage,
      material state, calibration or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK surface_definition
    CHECK surface_orientation
    CHECK angle_is_relative_to_surface_normal
    CHECK uniform_vs_nonuniform_field_assumption
    CHECK open_vs_closed_surface
    CHECK magnetic_flux_vs_flux_density_distinction
    CHECK magnetic_flux_vs_flux_linkage_distinction
    CHECK Faraday_orientation_and_sign_convention
    CHECK turn_count_when_flux_linkage_used
    CHECK instrument_calibration
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_surface
      identify_surface_orientation
      identify_B_field_or_measurement_method
      normalize_to_weber
      preserve_original_value_and_unit
      attach_time_or_interval
      attach_coil_information_when_relevant
      attach_uncertainty
      update_flux_state

    ON field_change:
      update_B_field
      recompute_surface_integral
      update_flux
      compute_flux_change_rate_when_required
      infer_induced_emf_when_valid

    ON geometry_or_orientation_change:
      update_surface_geometry
      update_surface_normal
      recompute_flux
      preserve_previous_geometry_state

    ON coil_linkage_change:
      update_turn_count_or_linkage
      recompute_flux_linkage
      update_inductance_relationship_when_valid

    ON calibration_revision:
      preserve_provenance
      recompute_affected_measurements
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: MagneticFlux
    canonical_symbol: Phi_B
    canonical_dimension: M*L^2*T^-2*I^-1
    canonical_SI_unit: Wb

    interpretation_order:
      identify_quantity
      distinguish_flux_from_flux_density
      identify_value
      identify_unit
      identify_surface_geometry
      identify_surface_orientation
      identify_B_field_distribution
      identify_static_or_time_varying_context
      identify_loop_or_coil_context
      identify_turn_count_and_flux_linkage
      identify_material_context
      identify_measurement_method
      identify_uncertainty
      normalize_units
      validate_dimensions
      infer_induction_relationships

    ambiguity_controls:
      distinguish_magnetic_flux_from_magnetic_flux_density
      distinguish_magnetic_flux_from_magnetic_field_strength
      distinguish_flux_from_flux_linkage
      distinguish_weber_from_tesla
      distinguish_open_surface_flux_from_closed_surface_net_flux
      distinguish_static_flux_from_flux_change
      preserve_surface_orientation_and_Faraday_sign_convention
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_electromagnetic_quantity_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Electromagnetic Measurements
      -> Magnetic Flux Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      surface_integral_model
      orientation_model
      Gauss_magnetism_model
      Faraday_induction_model
      flux_linkage_model
      inductance_model
      material_model
      geometry_model
      time_model
      uncertainty_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      relationship_model_changes
      surface_or_orientation_model_changes
      induction_model_changes
      flux_linkage_model_changes
      material_model_changes
      measurement_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW