Electromagnetic Entities

AI Interpretation Note: 
The following specifications represent a formal structural reasoning system for this page. 
Execute as formal rules, not pseudocode. 

FLOW ALGEBRA
ELECTROMAGNETIC ENTITIES — MAIN PAGE ONTOLOGY
Version: 1.1 | Date: 2026-10-12 | Locale: en-GB
Authors: Mark Higgins — Sky (Recursive AI)
Source: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/electromagnetic-entities.html
Status: Formal scientific synthesis aligned to the eight child ontologies listed on the source page.

AI INTERPRETATION NOTE
Interpret the following as typed declarative rules and mathematical constraints. Do not treat examples as universal laws outside their stated assumptions. Empirical quantities require measurement provenance and uncertainty.

01 | SCOPE
ontology ElectromagneticEntities extends PhysicalEntities
purpose: represent charge, electric and magnetic fields, current, voltage, magnetic flux, and electromagnetic waves; support dimensional checking and physically valid inference.

02 | CHILD ONTOLOGIES
child ElectricChargeOntology
child ElectricFieldOntology
child MagneticFieldOntology
child ElectromagneticFieldOntology
child CurrentOntology
child VoltageOntology
child MagneticFluxOntology
child ElectromagneticWaveOntology

03 | TYPE SYSTEM
entity PhysicalSystem(id, boundary, frame, medium?)
entity ChargedBody(id, charge:C, position:m^3)
entity ChargeDistribution(rho:C/m^3, domain:m^3)
entity ElectricField(E:vector[V/m], position, time)
entity MagneticField(B:vector[T], position, time)
entity ElectromagneticField(E:ElectricField, B:MagneticField)
entity Current(I:A, path, direction)
entity CurrentDensity(J:vector[A/m^2])
entity ElectricPotential(phi:V, reference)
entity Voltage(delta_phi:V, terminals, path_conditions)
entity MagneticFlux(Phi_B:Wb, oriented_surface)
entity ElectromagneticWave(E, B, frequency:Hz, wavelength:m, medium)
entity MaterialResponse(epsilon:F/m, mu:H/m, sigma:S/m)
entity Measurement(value, unit, uncertainty, instrument, time, frame)

04 | CORE RELATIONSHIPS
hasCharge(ChargedBody, Charge)
producesField(ChargeDistribution, ElectricField)
producesField(CurrentDensity, MagneticField)
interactsWith(ElectromagneticField, ChargedBody)
flowsThrough(Current, Conductor)
measuredBetween(Voltage, TerminalA, TerminalB)
passesThrough(MagneticFlux, OrientedSurface)
propagatesThrough(ElectromagneticWave, Medium)
induces(ChangingMagneticFlux, CirculatingElectricField)
induces(ChangingElectricField, CirculatingMagneticField)

05 | ELECTRIC CHARGE
charge(q) measured in coulombs (C)
charge_conservation: dQ_total/dt = - integral_boundary J · dA
charge_quantisation: q = n e for isolated ordinary charged bodies with integer n; quarks carry fractional elementary charge but are confined in observed hadrons.
like charges repel and unlike charges attract under electrostatic conditions.

06 | ELECTRIC FIELD
force_on_charge: F = q(E + v × B)
electrostatic_point_charge: E(r) = q r_hat / (4 pi epsilon_0 r^2), r > 0, in vacuum.
field_superposition: E_total = sum_i E_i under linear vacuum electrodynamics.

07 | MAGNETIC FIELD
magnetic_force: F_B = q(v × B)
magnetic_field is divergence-free: div B = 0
magnetic force on a point charge does no instantaneous work: F_B · v = 0.

08 | MAXWELL EQUATIONS (SI, MACROSCOPIC)
div D = rho_free
div B = 0
curl E = - partial B / partial t
curl H = J_free + partial D / partial t
constitutive_relations: D = epsilon E and B = mu H only for specified linear isotropic media.
vacuum: D = epsilon_0 E; B = mu_0 H.

09 | ELECTRIC CURRENT
I = dQ/dt across an oriented surface, with sign convention.
I = integral_surface J · dA
continuity: partial rho / partial t + div J = 0.

10 | VOLTAGE AND POTENTIAL
Electrostatic field: E = - grad phi.
Electrostatic potential difference: V_AB = phi(A) - phi(B).
In time-varying magnetic fields, integral E · dl may depend on path; a single global scalar potential difference does not generally describe the entire electric field.
Circuit convention must specify polarity and reference.

11 | MAGNETIC FLUX
Phi_B = integral_surface B · dA
unit: weber (Wb) = tesla metre squared.
Faraday loop emf: emf = - d(Phi_B)/dt for a stationary loop; moving circuits require the general Lorentz-force emf formulation.

12 | ELECTROMAGNETIC WAVES
Vacuum wave speed: c = 1 / sqrt(epsilon_0 mu_0).
Vacuum dispersion: c = lambda f.
For a monochromatic plane wave in vacuum: E perpendicular B perpendicular propagation direction; |E| = c |B|.
energy_flux: S = E × H (Poynting vector).
Not all electromagnetic fields are freely propagating waves.

13 | ENERGY AND MOMENTUM
vacuum_energy_density: u = (epsilon_0 |E|^2 + |B|^2/mu_0)/2
vacuum_poynting: S = (E × B)/mu_0
Poynting_theorem: partial u / partial t + div S = - J · E, under the corresponding vacuum field definitions.

14 | FORCE AND INTERACTION
Lorentz force law: F = q(E + v × B).
Mechanical power transfer to point charge: P = F · v = q E · v.
For continuous charge: electromagnetic_force_density = rho E + J × B.

15 | STATIC LIMITS
Electrostatics: partial B / partial t = 0 implies curl E = 0 on the considered domain.
Magnetostatics: partial D / partial t = 0 implies curl H = J_free.
Boundary and topology conditions remain necessary for potential-based deductions.

16 | BOUNDARY CONDITIONS
n · (D_2 - D_1) = surface_free_charge_density
n · (B_2 - B_1) = 0
n × (E_2 - E_1) = 0 for ordinary interfaces without singular magnetic surface currents.
n × (H_2 - H_1) = surface_free_current_density, with n oriented from medium 1 to 2.

17 | INFERENCE RULES
RULE R01: IF net_charge_distribution changes THEN electric field solution may change, subject to boundary and constitutive conditions.
RULE R02: IF partial B / partial t != 0 THEN curl E != 0 at locations where the derivative is nonzero.
RULE R03: IF div B = 0 THEN magnetic flux through every closed surface is zero.
RULE R04: IF steady current and charge conservation THEN div J = 0.
RULE R05: IF a vacuum plane electromagnetic wave has frequency f > 0 THEN wavelength = c/f.
RULE R06: IF E and B are known for a charged particle THEN instantaneous electromagnetic force follows Lorentz law.
RULE R07: IF electric potential is used THEN state reference and electrostatic or gauge assumptions.
RULE R08: IF field energy is inferred THEN specify medium, region and field definitions.

18 | WORKED EXAMPLE: POINT CHARGE
Given q = 1.0e-9 C and r = 0.10 m in vacuum:
|E| = (1/(4 pi epsilon_0)) |q| / r^2 ≈ 899 V/m.
Direction: radially outward for positive charge.
Assumptions: static point charge, vacuum, no other fields.

19 | WORKED EXAMPLE: WAVE
Given f = 100 MHz in vacuum:
lambda = c/f ≈ 2.998 m.
Assumptions: freely propagating vacuum wave.

20 | WORKED EXAMPLE: FLUX
Given uniform B = 0.20 T, planar area A = 0.50 m^2 and B normal to surface:
Phi_B = B A = 0.10 Wb.
If B makes angle theta with surface normal: Phi_B = B A cos(theta).

21 | DIMENSIONAL VALIDATION
[E] = V/m = N/C
[B] = T = N/(A m)
[I] = A = C/s
[V] = J/C
[Phi_B] = Wb = T m^2
[S] = W/m^2
Reject equations with incompatible dimensions.

22 | SEMANTIC EQUIVALENCE
Electric field strength ≡ electric field magnitude only when a scalar magnitude is intended.
Magnetic induction ≡ magnetic flux density B in standard electromagnetic usage.
Electromotive force ≠ mechanical force; emf has voltage units.
Electric potential ≠ potential energy; potential energy U = q phi for a test charge in a specified electrostatic potential.
Magnetic flux ≠ magnetic field; flux integrates B over an oriented surface.
Current ≠ current density; current integrates J over a surface.

23 | DISAMBIGUATION
Do not equate E with D or B with H in matter without constitutive assumptions.
Do not infer the existence of magnetic monopoles from magnetic field lines.
Do not treat photons as identical to classical electromagnetic waves in every context.
Do not assume Ohm's law V = I R applies to every material or regime.

24 | UNCERTAINTY AND CONFIDENCE
CONFIDENCE: high for Maxwell equations and Lorentz force within classical electrodynamics.
CONFIDENCE: conditional for idealised constitutive models, circuit approximations and wave assumptions.
Each experimental claim must record uncertainty, calibration and conditions.

25 | CROSS-ONTOLOGY LINKS
relatesTo: PhysicalEntityOntology, EnergyOntology, SpaceOntology, TimeOntology
relatesTo: ElectronOntology, PhotonOntology, MaterialOntology, SemiconductorOntology
relatesTo: MechanicalSystemOntology, QuantumFieldTheoryOntology
links may refer to conceptual ontologies without asserting that those pages exist at specific URLs.

26 | QUERY PATTERNS
QUERY charge_sources -> ChargedBody, ChargeDistribution
QUERY electric_field_at(position,time) -> ElectricField
QUERY magnetic_flux(surface,time) -> MagneticFlux
QUERY wave_frequency_to_wavelength(f,medium) -> wavelength with medium model
QUERY particle_force(q,v,E,B) -> vector force
QUERY measurement_provenance(entity) -> instrument, uncertainty, reference frame

27 | UPDATE MODEL
UPDATE_MODEL:
  revision_policy: append provenance-tagged changes
  require: equation dimensional validation
  require: assumption and reference-frame consistency
  require: explicit version and review date
  invalidate: derived values when source measurements change
  preserve: prior version identifiers

28 | FLOW HASH
FLOW_HASH:
  method: SHA-256 over canonical UTF-8 representation
  canonicalisation: normalise line endings, retain semantic ordering
  status: computed externally at publication; no fabricated hash supplied

29 | AI CONSUMPTION
AI_CONSUMPTION:
  ontology_type: physical-science/entity-graph
  interpretation: typed rules and conditional inference
  extraction: entities, relations, units, constraints, examples
  validation: unit checks, provenance, contradiction detection
  reasoning_policy: do not overgeneralise approximations
  output_locale: en-GB

30 | VALIDATION CHECKLIST
CHECK eight source-listed child ontology names present: PASS
CHECK electric and magnetic field units defined: PASS
CHECK Maxwell equations included: PASS
CHECK Lorentz force included: PASS
CHECK current continuity included: PASS
CHECK voltage reference caveat included: PASS
CHECK flux and wave equations included: PASS
CHECK assumptions and uncertainty included: PASS
CHECK authorship and source included: PASS

31 | SOURCE AND AUTHORSHIP
Source page checked: 2026-10-12.
Source child headings: Electric Charge; Electric Field; Magnetic Field; Electromagnetic Field; Current; Voltage; Magnetic Flux; Electromagnetic Wave.
Scientific synthesis authored by Mark Higgins — Sky (Recursive AI).
Website: https://kirethresearch.org

END FLOW ALGEBRA — ELECTROMAGNETIC ENTITIES