Electric Potential Ontology

# Electric Potential Ontology — Flow Algebra

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

FLOW ElectricPotentialOntology {

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

  PURPOSE:
    Represent electric potential as a measurable scalar electromagnetic quantity describing potential energy per unit electric charge relative to a defined reference, including electric potential difference, voltage, electric fields, electrostatic potential energy, units, dimensional structure, reference conditions, spatial variation, measurement methods, uncertainty, and distinctions from charge, electric field and energy.

  ENTITY ElectricPotential {
    TYPE: DerivedElectromagneticQuantity
    SYMBOL: V
    DIMENSION: M * L^2 * T^-3 * I^-1
    SI_UNIT: volt
    SI_SYMBOL: V

    DEFINITION:
      electric_potential := electric_potential_energy_per_unit_charge

    ENERGY_RELATION:
      V = U / q
      WHEN q != 0

    FIELD_RELATION:
      E = -gradient(V)
      UNDER electrostatic_or_scalar_potential_context

    PROPERTIES:
      is_scalar
      has_value
      has_unit
      has_dimension
      requires_reference_level_for_absolute_numeric_value
      potential_difference_is_reference_independent_for_common_offset
      may_vary_with_position
      may_vary_with_time
      may_have_uncertainty
  }

  ENTITY ElectricPotentialDifference {
    TYPE: DerivedElectromagneticQuantity
    ALIAS: Voltage
    SYMBOL: delta_V
    SI_UNIT: volt
    SI_SYMBOL: V

    DEFINITION:
      potential_difference := potential_at_B - potential_at_A

    FORM:
      delta_V = V_B - V_A
  }

  ENTITY ElectricPotentialEnergy {
    TYPE: EnergyQuantity
    SYMBOL: U
    DIMENSION: M * L^2 * T^-2
    SI_UNIT: joule
    SI_SYMBOL: J

    RELATION:
      U = q*V
      UNDER defined_reference
  }

  ENTITY ElectricCharge {
    TYPE: DerivedElectromagneticQuantity
    SYMBOL: q
    DIMENSION: I*T
    SI_UNIT: coulomb
    SI_SYMBOL: C

    RELATION:
      ElectricPotentialEnergy / ElectricCharge -> ElectricPotential
  }

  ENTITY ElectricField {
    TYPE: VectorFieldQuantity
    SYMBOL: E
    SI_UNIT: volt_per_metre
    SI_SYMBOL: V/m

    ELECTROSTATIC_RELATION:
      E = -gradient(V)
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: volt
      symbol: V

      equivalence:
        1 V = 1 J/C
        1 V = 1 W/A
        1 V = 1 kg*m^2/(A*s^3)
    }

    COMMON_ALTERNATIVES {
      microvolt
      millivolt
      kilovolt
      megavolt
    }

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

  CLASSIFICATION {
    by_semantic_role:
      electric_potential
      electric_potential_difference
      voltage

    by field_context:
      electrostatic_potential
      time_varying_electric_potential

    by reference:
      potential_relative_to_ground
      potential_relative_to_reference_node
      potential_relative_to_infinity
      potential_difference_between_nodes
  }

  REFERENCE_MODEL {
    PRINCIPLE:
      electric_potential_numeric_value requires_defined_zero_or_reference

    COMMON_REFERENCES:
      ground
      circuit_reference_node
      infinity_for_localised_electrostatic_system
      arbitrary_zero_surface

    GAUGE_FREEDOM_ELECTROSTATIC:
      V_prime = V + constant
      produces_same_electric_field

    POTENTIAL_DIFFERENCE:
      delta_V unaffected_by_common_constant_offset

    RULE:
      potential_values_from_different_reference_levels
      MUST_NOT be directly_compared_without_reference_alignment
  }

  POTENTIAL_DIFFERENCE_MODEL {
    DEFINITION:
      delta_V_AB = V_B - V_A

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

    PATH_INDEPENDENCE:
      applies_when_electric_field_is_conservative

    RULE:
      in_time_varying_electromagnetic_fields
      simple_scalar_potential_difference_interpretation
      MAY require_vector_potential_and_path_context
  }

  ELECTRIC_FIELD_MODEL {
    ELECTROSTATIC:
      E = -gradient(V)

    ONE_DIMENSION:
      E_x = -dV/dx

    UNIFORM_FIELD_APPROXIMATION:
      delta_V = -E dot delta_r

    RULE:
      electric_field_is_vector
      electric_potential_is_scalar
  }

  POINT_CHARGE_MODEL {
    POTENTIAL_IN_VACUUM:
      V(r) = (1/(4*pi*epsilon_0)) * q/r

    CONDITIONS:
      point_charge
      electrostatic_context
      reference V(infinity) = 0
      r > 0

    SUPERPOSITION:
      V_total = sum(V_i)

    RULE:
      scalar_potentials_add_algebraically
  }

  CONTINUOUS_CHARGE_MODEL {
    GENERAL_ELECTROSTATIC_POTENTIAL:
      V(r) =
        (1/(4*pi*epsilon_0))
        * integral(rho_q(r_prime)/|r-r_prime| dV_prime)

    CONDITIONS:
      electrostatic_vacuum_context
      appropriate_boundary_conditions

    RULE:
      charge_distribution_and_boundary_conditions
      determine_potential_solution
  }

  ENERGY_MODEL {
    PARTICLE_RELATION:
      U = q*V

    CHANGE:
      delta_U = q*delta_V
      WHEN q_constant

    WORK_BY_ELECTRIC_FIELD:
      W_field = -delta_U

    FOR_CONSTANT_CHARGE:
      W_field = -q*delta_V

    RULE:
      charge_sign MUST be preserved
      when inferring potential_energy_or_work
  }

  CIRCUIT_MODEL {
    NODE_POTENTIAL:
      voltage_at_node = potential_relative_to_reference_node

    BRANCH_VOLTAGE:
      V_AB = V_A - V_B
      according_to_defined_polarity

    KIRCHHOFF_VOLTAGE:
      algebraic_sum(voltage_changes_around_closed_loop) = 0
      UNDER lumped_circuit_assumptions

    RULE:
      voltage polarity_and_reference_node
      MUST be preserved
  }

  RELATIONSHIPS {
    ElectricPotential -> ENERGY_PER_CHARGE -> ElectricPotentialEnergy
    ElectricPotential -> HAS_DIMENSION -> M*L^2*T^-3*I^-1
    ElectricPotential -> MEASURED_IN -> Volt
    ElectricPotentialDifference -> DIFFERENCE_OF -> ElectricPotentialValues
    Voltage -> SEMANTICALLY_EQUIVALENT_TO -> ElectricPotentialDifference
    ElectricField -> NEGATIVE_GRADIENT_OF -> ElectricPotential
    ElectricPotentialEnergy -> PRODUCT_OF -> ChargeAndPotential
    ChargeDistribution -> GENERATES -> ElectricPotential
    BoundaryConditions -> CONSTRAIN -> ElectricPotential
  }

  SEMANTIC_EQUIVALENCE {
    "electric potential" ~= electrostatic_potential WHEN electrostatic_context
    "electric potential difference" ~= voltage
    "potential difference" ~= voltage WHEN electrical_context
    "volt" ~= "V"
    "joule per coulomb" ~= "J/C"

    electric_potential != electric_potential_energy
    electric_potential != electric_field
    electric_potential != electric_charge
    electric_potential_difference != absolute_reference_potential
  }

  CONSTRAINTS {
    electric_potential_is_scalar = true
    dimensional_formula = M*L^2*T^-3*I^-1
    SI_unit = V
    electric_potential_numeric_value_requires_reference = true
    potential_difference_requires_two_defined_points_or_nodes = true
    electric_field_and_potential_are_not_semantically_equivalent = true
    potential_and_potential_energy_are_not_semantically_equivalent = true
    voltage_polarity_must_be_preserved = true
    electrostatic_gradient_relation_requires_applicable_field_context = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE:
      ElectricPotentialDifference

    COMMON_INSTRUMENTS:
      voltmeter
      digital_multimeter
      oscilloscope
      electrometer
      differential_probe
      electrostatic_voltmeter

    MEASUREMENT_CONTEXT:
      most_instruments_measure_potential_difference
      rather_than_reference_free_absolute_potential

    RECORD:
      numerical_value
      unit
      positive_node_or_point
      negative_node_or_point
      reference_node
      polarity
      AC_or_DC
      RMS_peak_average_or_instantaneous
      frequency_when_relevant
      timestamp
      instrument
      input_impedance
      calibration_state
      uncertainty

    UNCERTAINTY:
      measured_potential_difference = best_estimate +/- uncertainty
  }

  REASONING_RULES {
    IF potential_energy_known AND charge_known AND charge != 0
      THEN electric_potential = potential_energy / charge

    IF electric_potential_known AND charge_known
      THEN electric_potential_energy = charge * electric_potential
      UNDER defined_reference

    IF potentials_at_A_and_B_known
      THEN potential_difference_AB = potential_B - potential_A

    IF conservative_electric_field_known_along_path
      THEN potential_difference =
        -line_integral(electric_field dot differential_path)

    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
      AND reference_at_infinity
      THEN potential =
        (1/(4*pi*epsilon_0))*charge/distance

    IF multiple_electrostatic_source_potentials_known
      THEN total_potential = algebraic_sum(source_potentials)

    IF constant_charge_known AND potential_difference_known
      THEN potential_energy_change = charge * potential_difference
  }

  TIME_VARYING_FIELD_MODEL {
    GENERAL_POTENTIAL_REPRESENTATION:
      E = -gradient(phi) - partial(A_vector)/partial(t)

    scalar_potential:
      phi

    vector_potential:
      A_vector

    RULE:
      in_time_varying_fields
      E MUST_NOT generally_be_inferred_from_scalar_potential_gradient_alone
  }

  UNCERTAINTY_MODEL {
    sources:
      instrument_resolution
      calibration_uncertainty
      input_loading
      probe_impedance
      reference_node_noise
      contact_potential
      lead_and_connection_effects
      electromagnetic_interference
      sampling_and_bandwidth

    PROPAGATION:
      derived_potential_uncertainty
      <- input_measurement_uncertainties_and_model
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    electrostatic_field_relationship_confidence: 1.00
    reference_model_confidence: 1.00
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when reference level, polarity,
      measurement points, AC/DC context, frequency,
      instrument loading, calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK reference_level
    CHECK measurement_points_or_nodes
    CHECK polarity
    CHECK scalar_vs_vector_semantics
    CHECK potential_vs_potential_energy_distinction
    CHECK potential_vs_electric_field_distinction
    CHECK electrostatic_vs_time_varying_field_context
    CHECK AC_DC_and_RMS_peak_semantics_when_relevant
    CHECK instrument_loading_when_measured
    CHECK instrument_calibration
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      identify_measurement_points
      identify_reference_node
      identify_polarity
      normalize_to_volt
      preserve_original_value_and_unit
      identify_AC_or_DC_context
      attach_frequency_when_relevant
      attach_timestamp
      attach_uncertainty
      update_potential_state

    ON reference_change:
      record_old_reference
      record_new_reference
      transform_potential_values
      preserve_potential_differences_when_common_offset_applies
      update_provenance

    ON field_or_charge_distribution_change:
      update_sources
      update_boundary_conditions
      recompute_potential_field_when_model_available
      recompute_electric_field_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: ElectricPotential
    canonical_symbol: V
    canonical_dimension: M*L^2*T^-3*I^-1
    canonical_SI_unit: volt

    interpretation_order:
      identify_quantity
      distinguish_potential_from_potential_difference
      identify_value
      identify_unit
      identify_reference_level
      identify_points_or_nodes
      identify_polarity
      identify_charge_or_energy_context
      identify_electric_field_context
      identify_electrostatic_or_time_varying_context
      identify_AC_or_DC_measurement_context
      identify_measurement_method
      identify_uncertainty
      normalize_units
      validate_dimensions
      infer_relationships

    ambiguity_controls:
      distinguish_electric_potential_from_voltage_when_reference_semantics_matter
      distinguish_potential_from_potential_energy
      distinguish_potential_from_electric_field
      distinguish_potential_from_charge
      distinguish_absolute_reference_value_from_potential_difference
      distinguish_electrostatic_scalar_potential_from_general_time_varying_potential_representation
      preserve_voltage_polarity_and_reference_node
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_electromagnetic_quantity_semantics

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

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      reference_model
      potential_difference_model
      electric_field_model
      point_charge_model
      continuous_charge_model
      energy_model
      circuit_model
      time_varying_field_model
      uncertainty_model
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      relationship_model_changes
      reference_model_changes
      field_model_changes
      circuit_model_changes
      measurement_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW