Electric Field Ontology

# Electric Field Ontology — Flow Algebra

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

FLOW ElectricFieldOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Electromagnetic Measurements
    -> Electric Field Ontology

  PURPOSE:
    Represent the electric field as a measurable vector electromagnetic field describing electric force per unit positive test charge, including field magnitude and direction, electric potential relationships, charge distributions, electric flux, superposition, units, dimensional structure, spatial and temporal variation, material effects, measurement methods, uncertainty, and distinctions from electric potential, electric displacement field and force.

  ENTITY ElectricField {
    TYPE: VectorFieldPhysicalQuantity
    SYMBOL: E
    DIMENSION: M * L * T^-3 * I^-1
    SI_UNIT: volt_per_metre
    SI_SYMBOL: V/m

    FORCE_DEFINITION:
      E = F_electric / q
      WHEN q != 0 AND test_charge_limit_applies

    ELECTROSTATIC_POTENTIAL_RELATION:
      E = -gradient(V)

    GENERAL_POTENTIAL_RELATION:
      E = -gradient(phi) - partial(A_vector)/partial(t)

    PROPERTIES:
      is_vector_field
      has_magnitude
      has_direction
      has_unit
      has_dimension
      varies_with_position
      may_vary_with_time
      obeys_superposition_in_linear_classical_context
      may_have_uncertainty
  }

  ENTITY ElectricForce {
    TYPE: VectorPhysicalQuantity
    SYMBOL: F_e
    SI_UNIT: newton
    SI_SYMBOL: N

    RELATION:
      F_e = q*E
  }

  ENTITY ElectricCharge {
    TYPE: DerivedElectromagneticQuantity
    SYMBOL: q
    SI_UNIT: coulomb
    SI_SYMBOL: C

    RELATION:
      charge_distribution -> source_of_electric_field
  }

  ENTITY ElectricPotential {
    TYPE: ScalarFieldQuantity
    SYMBOL: V
    SI_UNIT: volt
    SI_SYMBOL: V

    ELECTROSTATIC_RELATION:
      E = -gradient(V)
  }

  ENTITY ElectricFluxDensity {
    ALIAS: ElectricDisplacementField
    TYPE: VectorFieldQuantity
    SYMBOL: D
    SI_UNIT: coulomb_per_square_metre
    SI_SYMBOL: C/m^2

    LINEAR_ISOTROPIC_RELATION:
      D = epsilon*E
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: volt_per_metre
      symbol: V/m

      equivalence:
        1 V/m = 1 N/C
        1 V/m = 1 kg*m/(A*s^3)
    }

    COMMON_ALTERNATIVES {
      newton_per_coulomb
      volt_per_centimetre
      kilovolt_per_metre
      kilovolt_per_centimetre
      megavolt_per_metre
    }

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

  CLASSIFICATION {
    by_time:
      electrostatic_field
      time_varying_electric_field

    by spatial_structure:
      uniform_electric_field
      nonuniform_electric_field
      radial_electric_field
      local_electric_field

    by source_context:
      point_charge_field
      distributed_charge_field
      induced_electric_field

    by material_context:
      vacuum_electric_field
      dielectric_electric_field
  }

  POINT_CHARGE_MODEL {
    VACUUM_FIELD:
      E_vector =
        (1/(4*pi*epsilon_0))
        * q/r^2
        * r_hat

    CONDITIONS:
      point_charge
      electrostatic_context
      vacuum
      r > 0

    DIRECTION:
      q > 0 -> radially_outward
      q < 0 -> radially_inward
  }

  SUPERPOSITION_MODEL {
    DISCRETE_SOURCES:
      E_total = vector_sum(E_i)

    CONTINUOUS_DISTRIBUTION:
      E(r) =
        (1/(4*pi*epsilon_0))
        * integral(
            rho_q(r_prime)
            * (r-r_prime)
            / |r-r_prime|^3
            dV_prime
          )

    CONDITIONS:
      classical_linear_electromagnetic_context

    RULE:
      field_components MUST be vector_summed
      not scalar_magnitudes_added_unconditionally
  }

  GAUSS_LAW_MODEL {
    DIFFERENTIAL_FORM:
      divergence(E) = rho/epsilon_0
      IN vacuum

    INTEGRAL_FORM:
      closed_surface_integral(E dot dA)
        = Q_enclosed/epsilon_0
      IN vacuum

    MATERIAL_FORM:
      divergence(D) = rho_free

    RULE:
      symmetry_can_enable_field_inference
      but Gauss_law_validity_does_not_depend_on_symmetry
  }

  POTENTIAL_MODEL {
    ELECTROSTATIC:
      E = -gradient(V)

    POTENTIAL_DIFFERENCE:
      V_B - V_A = -integral_A_to_B(E dot dl)

    CONSERVATIVE_PROPERTY:
      curl(E) = 0
      IN electrostatic_context

    RULE:
      electrostatic_line_integral_is_path_independent
  }

  TIME_VARYING_FIELD_MODEL {
    FARADAY_RELATION:
      curl(E) = -partial(B)/partial(t)

    POTENTIAL_REPRESENTATION:
      E = -gradient(phi) - partial(A_vector)/partial(t)

    CONSEQUENCE:
      electric_field_need_not_be_conservative

    RULE:
      E MUST_NOT generally_be_inferred_from_scalar_potential_gradient_alone
      in_time_varying_electromagnetic_context
  }

  ELECTRIC_FLUX_MODEL {
    ELECTRIC_FLUX:
      Phi_E = surface_integral(E dot dA)

    UNIFORM_PLANAR_CASE:
      Phi_E = E*A*cos(theta)

    PROPERTY:
      flux_is_scalar_surface_integral_result

    RULE:
      electric_flux != electric_flux_density
  }

  MATERIAL_MODEL {
    LINEAR_ISOTROPIC_DIELECTRIC:
      D = epsilon*E

    PERMITTIVITY:
      epsilon = epsilon_r*epsilon_0

    POLARISATION_RELATION:
      D = epsilon_0*E + P

    RULE:
      field_material_relationship depends_on constitutive_model
  }

  FORCE_MODEL {
    STATIONARY_CHARGE:
      F = q*E

    MOVING_CHARGE_GENERAL_LORENTZ:
      F = q*(E + v cross B)

    RULE:
      electric_field_component_of_force
      MUST be distinguished_from magnetic_force_component
  }

  ENERGY_MODEL {
    POTENTIAL_ENERGY_CHANGE:
      delta_U = q*delta_V

    LINEAR_DIELECTRIC_FIELD_ENERGY_DENSITY:
      u_E = 0.5*(E dot D)

    VACUUM:
      u_E = 0.5*epsilon_0*|E|^2

    CONDITIONS:
      applicable_linear_nondispersive_context
  }

  RELATIONSHIPS {
    ElectricField -> FORCE_PER_UNIT_CHARGE -> ElectricForce
    ElectricField -> HAS_DIMENSION -> M*L*T^-3*I^-1
    ElectricField -> MEASURED_IN -> VoltPerMetre
    ElectricCharge -> SOURCE_OF -> ElectricField
    ElectricField -> NEGATIVE_GRADIENT_OF -> ElectricPotential
    ElectricFlux -> SURFACE_INTEGRAL_OF -> ElectricField
    ElectricDisplacementField -> RELATED_TO -> ElectricField
    Permittivity -> RELATES -> ElectricFieldAndDisplacementField
    TimeVaryingMagneticField -> INDUCES -> ElectricField
    ElectricField -> CONTRIBUTES_TO -> LorentzForce
  }

  SEMANTIC_EQUIVALENCE {
    "electric field" ~= "electric field strength"
    "volt per metre" ~= "V/m"
    "newton per coulomb" ~= "N/C"
    "V/m" ~= "N/C"

    electric_field != electric_potential
    electric_field != electric_force
    electric_field != electric_flux
    electric_field != electric_flux_density
    electric_field != electric_displacement_field
  }

  CONSTRAINTS {
    electric_field_is_vector = true
    dimensional_formula = M*L*T^-3*I^-1
    SI_unit = V/m
    force_definition_requires_nonzero_test_charge = true
    test_charge_should_not_materially_perturb_source_configuration = true
    electric_field_and_potential_are_not_semantically_equivalent = true
    electric_field_and_displacement_field_are_not_semantically_equivalent = true
    field_vector_direction_must_be_preserved = true
    electrostatic_gradient_relation_requires_applicable_context = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE_OR_INFERRED:
      ElectricField

    COMMON_MEASUREMENT_METHODS:
      electric_field_meter
      field_mill
      electrostatic_fieldmeter
      calibrated_E_field_probe
      antenna_probe
      potential_gradient_inference
      force_on_known_test_charge

    RECORD:
      vector_value_or_magnitude
      unit
      direction
      coordinate_components
      spatial_location
      timestamp
      electrostatic_or_time_varying
      frequency
      phase_when_relevant
      material_or_medium
      temperature_when_relevant
      instrument
      probe_orientation
      bandwidth
      calibration_state
      uncertainty

    UNCERTAINTY:
      measured_or_inferred_electric_field = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF electric_force_known AND charge_known AND charge != 0
      THEN electric_field = electric_force / charge
      UNDER test_charge_context

    IF electric_field_known AND charge_known
      THEN electric_force = charge * electric_field

    IF electrostatic_potential_field_known
      THEN electric_field = -gradient(electric_potential)

    IF point_charge_known AND distance_known AND distance > 0
      AND vacuum_electrostatic_conditions_apply
      THEN electric_field =
        (1/(4*pi*epsilon_0))*charge/distance^2 * radial_unit_vector

    IF multiple_source_fields_known
      THEN total_electric_field = vector_sum(source_fields)

    IF electric_field_known_over_surface
      THEN electric_flux = surface_integral(electric_field dot differential_area)

    IF linear_isotropic_permittivity_known AND electric_field_known
      THEN electric_displacement_field = permittivity * electric_field

    IF magnetic_flux_density_changes_with_time
      THEN induced_electric_field_may_have_nonzero_curl
  }

  FIELD_REPRESENTATION_MODEL {
    electric_field:
      E = E(x, y, z, t)

    cartesian_components:
      E = (E_x, E_y, E_z)

    magnitude:
      |E| = sqrt(E_x^2 + E_y^2 + E_z^2)

    direction:
      E_hat = E/|E|
      WHEN |E| != 0
  }

  REFERENCE_FRAME_MODEL {
    electromagnetic_fields:
      electric_and_magnetic_fields_depend_on_reference_frame
      under_relativistic_transformations

    RULE:
      electric_field_values_from_different_inertial_frames
      MUST_NOT be assumed_identical

    REQUIRE_WHEN_RELEVANT:
      reference_frame
      observer_motion
  }

  UNCERTAINTY_MODEL {
    sources:
      probe_calibration
      probe_orientation
      spatial_position
      field_nonuniformity
      bandwidth
      frequency_response
      environmental_coupling
      probe_perturbation
      electromagnetic_interference
      model_assumptions

    PROPAGATION:
      derived_field_uncertainty
      <- input_uncertainties_and_field_model
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    electrostatic_relationship_confidence: 1.00
    Maxwell_relationship_confidence: 1.00
    measurement_context_confidence: 0.97

    RULE:
      confidence decreases when field direction, spatial location,
      time/frequency context, material, reference frame,
      probe orientation, calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK vector_direction_and_components
    CHECK spatial_location
    CHECK electrostatic_vs_time_varying_context
    CHECK electric_field_vs_potential_distinction
    CHECK electric_field_vs_displacement_field_distinction
    CHECK electric_flux_vs_flux_density_distinction
    CHECK material_constitutive_model_when_used
    CHECK reference_frame_when_relevant
    CHECK probe_orientation_when_measured
    CHECK instrument_calibration
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_vector_or_magnitude_representation
      identify_direction_or_components
      attach_spatial_location
      attach_timestamp
      identify_electrostatic_or_time_varying_context
      attach_frequency_when_relevant
      identify_material_or_medium
      normalize_to_V_per_m
      preserve_original_value_and_unit
      attach_uncertainty
      update_field_state

    ON source_change:
      update_charge_distribution
      update_boundary_conditions
      recompute_electric_field_when_model_available
      update_potential_when_valid
      preserve_previous_state

    ON material_change:
      update_permittivity
      update_polarisation_model
      recompute_D_and_E_relationships
      preserve_material_provenance

    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: ElectricField
    canonical_symbol: E
    canonical_dimension: M*L*T^-3*I^-1
    canonical_SI_unit: V/m

    interpretation_order:
      identify_quantity
      identify_value_or_vector
      identify_unit
      identify_direction_and_components
      identify_spatial_location
      identify_time_or_frequency
      identify_charge_source_context
      identify_potential_context
      identify_material_or_medium
      identify_electrostatic_or_time_varying_context
      identify_reference_frame
      identify_measurement_method
      identify_uncertainty
      normalize_units
      validate_dimensions
      infer_field_relationships

    ambiguity_controls:
      distinguish_electric_field_from_electric_potential
      distinguish_electric_field_from_electric_force
      distinguish_electric_field_from_electric_flux
      distinguish_electric_field_from_electric_displacement_field
      distinguish_scalar_field_magnitude_from_vector_field
      distinguish_electrostatic_from_induced_electric_field
      preserve_spatial_direction_and_reference_frame
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_electromagnetic_quantity_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Electromagnetic Measurements
      -> Electric Field Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      point_charge_model
      superposition_model
      Gauss_law_model
      potential_model
      time_varying_field_model
      electric_flux_model
      material_model
      force_model
      energy_model
      field_representation_model
      reference_frame_model
      uncertainty_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      relationship_model_changes
      field_source_model_changes
      potential_model_changes
      material_model_changes
      measurement_model_changes
      reference_frame_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW