{"openapi":"3.1.0","info":{"title":"Coulomb & Electric Field API","version":"1.0.0","description":"Coulomb's-law electrostatics as an API, computed locally and deterministically. The force endpoint computes the electrostatic force between two point charges, F = k·q1·q2/(εr·r²) — Coulomb's law, with k = 8.9876×10⁹ N·m²/C² — from the two charges, their separation and an optional relative permittivity for a dielectric medium, and tells you whether the force is attractive (opposite signs) or repulsive (like signs). The field endpoint gives the electric field of a point charge, E = k·q/(εr·r²), its direction (away from a positive charge, toward a negative one), and the force on a test charge placed there, F = q_test·E. The potential endpoint gives the electric potential V = k·q/(εr·r) and, for a pair of charges, the electrostatic potential energy U = k·q1·q2/(εr·r) in joules and electron-volts. Charges may be entered in coulombs, microcoulombs or nanocoulombs. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics and electrical-engineering education tools, electrostatics and field-theory apps, and laboratory and simulation software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is electrostatics; for Ohm's law and DC/AC circuits use an Ohm's-law API.","contact":{"name":"PremiumApi","url":"https://www.oanor.com/by/premiumapi"}},"servers":[{"url":"https://api.oanor.com/coulomb-api","description":"oanor gateway"}],"tags":[{"name":"Electrostatics"},{"name":"Meta"}],"components":{"securitySchemes":{"oanorKey":{"type":"apiKey","in":"header","name":"x-oanor-key","description":"Get your key at https://www.oanor.com/developer/keys"}}},"security":[{"oanorKey":[]}],"paths":{"/v1/field":{"get":{"operationId":"get_v1_field","tags":["Electrostatics"],"summary":"Electric field of a point charge","description":"","parameters":[{"name":"charge","in":"query","required":true,"description":"Source charge (C)","schema":{"type":"string"},"example":"0.000001"},{"name":"distance","in":"query","required":true,"description":"Distance r (m)","schema":{"type":"string"},"example":"0.1"},{"name":"test_charge","in":"query","required":false,"description":"Test charge for the force (C)","schema":{"type":"string"}},{"name":"relative_permittivity","in":"query","required":false,"description":"Dielectric εr (default 1)","schema":{"type":"string"}}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"formula":"E = k·q/(εr·r²); force on a test charge F = q_test·E.","charge_c":1.0e-6,"distance_m":0.1,"field_direction":"away from the charge","electric_field_v_m":898755.17873682,"relative_permittivity":1,"electric_field_magnitude_v_m":898755.17873682},"meta":{"timestamp":"2026-06-04T10:18:45.739Z","request_id":"0a7652ae-c0ef-4d3c-8790-ba1d08839f1d"},"status":"ok","message":"Electric field","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/force":{"get":{"operationId":"get_v1_force","tags":["Electrostatics"],"summary":"Coulomb force between two charges","description":"","parameters":[{"name":"charge1","in":"query","required":true,"description":"Charge 1 (C)","schema":{"type":"string"},"example":"0.000001"},{"name":"charge2","in":"query","required":true,"description":"Charge 2 (C)","schema":{"type":"string"},"example":"0.000002"},{"name":"distance","in":"query","required":true,"description":"Separation r (m)","schema":{"type":"string"},"example":"0.1"},{"name":"relative_permittivity","in":"query","required":false,"description":"Dielectric εr (default 1)","schema":{"type":"string"},"example":"1"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"force_n":1.7975103575,"formula":"F = k·q1·q2/(εr·r²); k = 8.9876×10⁹ N·m²/C².","charge1_c":1.0e-6,"charge2_c":2.0e-6,"distance_m":0.1,"interaction":"repulsive","force_magnitude_n":1.7975103575,"relative_permittivity":1},"meta":{"timestamp":"2026-06-04T10:18:45.880Z","request_id":"6d55877c-c9b6-4648-9343-e211c5046f0b"},"status":"ok","message":"Coulomb force","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/potential":{"get":{"operationId":"get_v1_potential","tags":["Electrostatics"],"summary":"Electric potential & energy","description":"","parameters":[{"name":"charge","in":"query","required":true,"description":"Source charge (C)","schema":{"type":"string"},"example":"0.000001"},{"name":"distance","in":"query","required":true,"description":"Distance r (m)","schema":{"type":"string"},"example":"0.1"},{"name":"charge2","in":"query","required":false,"description":"Second charge for pair energy (C)","schema":{"type":"string"},"example":"0.000002"},{"name":"relative_permittivity","in":"query","required":false,"description":"Dielectric εr (default 1)","schema":{"type":"string"}}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"formula":"V = k·q/(εr·r); U = k·q1·q2/(εr·r).","charge_c":1.0e-6,"charge2_c":2.0e-6,"distance_m":0.1,"potential_energy_j":0.179751035747,"potential_energy_ev":1121917720760890100,"electric_potential_v":89875.51787368,"relative_permittivity":1},"meta":{"timestamp":"2026-06-04T10:18:45.971Z","request_id":"56a2633e-0e7d-41d2-8247-5c15b99da543"},"status":"ok","message":"Electric potential & energy","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/meta":{"get":{"operationId":"get_v1_meta","tags":["Meta"],"summary":"Spec","description":"","parameters":[],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"api":"coulomb","note":"Coulomb's law / electrostatics — computed locally and deterministically, no key, no third-party service.","constants":{"coulomb_constant":8987551787.368176,"elementary_charge":1.602176634e-19,"vacuum_permittivity":8.8541878128e-12},"endpoints":["/v1/force","/v1/field","/v1/potential","/v1/meta"]},"meta":{"timestamp":"2026-06-04T10:18:46.057Z","request_id":"75a740c9-7cd4-44c4-afb6-8f407475faad"},"status":"ok","message":"Meta","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}}},"x-oanor-pricing":[{"slug":"free","name":"Free","price_cents_month":0,"monthly_call_quota":2000,"rps_limit":2,"hard_limit":true},{"slug":"starter","name":"Starter","price_cents_month":500,"monthly_call_quota":25000,"rps_limit":5,"hard_limit":true},{"slug":"pro","name":"Pro","price_cents_month":1500,"monthly_call_quota":150000,"rps_limit":15,"hard_limit":true},{"slug":"mega","name":"Mega","price_cents_month":4900,"monthly_call_quota":765000,"rps_limit":40,"hard_limit":true}],"x-oanor-marketplace-url":"https://www.oanor.com/api/coulomb-api"}