Biot–Savart law
E625462
The Biot–Savart law is a fundamental equation in electromagnetism that gives the magnetic field produced by a steady electric current by integrating contributions from each current element in space.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Biot–Savart law canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6877169 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Biot–Savart law Context triple: [Ampère's force law, relatedTo, Biot–Savart law]
-
A.
Ampère's force law
Ampère's force law is a fundamental principle in electromagnetism that quantifies the mechanical force between electric currents in conductors.
-
B.
Ampère–Maxwell law
The Ampère–Maxwell law is one of Maxwell’s equations that relates magnetic fields to electric currents and changing electric fields, thereby introducing the concept of displacement current and enabling the prediction of electromagnetic waves.
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C.
Lorentz force
The Lorentz force is the fundamental force experienced by a charged particle moving in electric and magnetic fields, forming the basis of classical electromagnetism.
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D.
Gauss’s law
Gauss’s law is a fundamental principle of electromagnetism that relates the electric flux through a closed surface to the electric charge enclosed within that surface.
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E.
Gauss's law for magnetism
Gauss's law for magnetism is the Maxwell equation stating that magnetic monopoles do not exist and that magnetic field lines always form closed loops with zero net flux through any closed surface.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Biot–Savart law Target entity description: The Biot–Savart law is a fundamental equation in electromagnetism that gives the magnetic field produced by a steady electric current by integrating contributions from each current element in space.
-
A.
Ampère's force law
Ampère's force law is a fundamental principle in electromagnetism that quantifies the mechanical force between electric currents in conductors.
-
B.
Ampère–Maxwell law
The Ampère–Maxwell law is one of Maxwell’s equations that relates magnetic fields to electric currents and changing electric fields, thereby introducing the concept of displacement current and enabling the prediction of electromagnetic waves.
-
C.
Lorentz force
The Lorentz force is the fundamental force experienced by a charged particle moving in electric and magnetic fields, forming the basis of classical electromagnetism.
-
D.
Gauss’s law
Gauss’s law is a fundamental principle of electromagnetism that relates the electric flux through a closed surface to the electric charge enclosed within that surface.
-
E.
Gauss's law for magnetism
Gauss's law for magnetism is the Maxwell equation stating that magnetic monopoles do not exist and that magnetic field lines always form closed loops with zero net flux through any closed surface.
- F. None of above. chosen
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
equation in electromagnetism
ⓘ
physical law ⓘ |
| analogousTo |
Coulomb's law for electric fields
ⓘ
linked to:
Coulomb's law
|
| appliesTo |
quasi-static currents
ⓘ
steady currents ⓘ |
| assumes |
non-relativistic regime
ⓘ
steady or slowly varying currents ⓘ |
| constantInVacuum | μ₀ / 4π ⓘ |
| coordinateForm | vector form ⓘ |
| dependsOn | permeability of the medium ⓘ |
| describes | magnetic field produced by electric currents ⓘ |
| domain | classical electrodynamics ⓘ |
| expressedAs |
B(r) = (μ₀ / 4π) ∫ (I dℓ × (r − r′)) / |r − r′|³
ⓘ
dB = (μ₀ / 4π) * (I dℓ × r̂) / r² ⓘ |
| field | electromagnetism ⓘ |
| generalizedBy |
Liénard–Wiechert potentials
ⓘ
linked to:
Lienard–Wiechert potentials
|
| gives | differential contribution to magnetic field from each current element ⓘ |
| givesDirectionBy | right-hand rule ⓘ |
| inverselyProportionalTo | square of distance r² ⓘ |
| involvesOperation | line integral over current distribution ⓘ |
| involvesQuantity |
cross product of current element and displacement unit vector
ⓘ
distance between current element and field point ⓘ electric current ⓘ magnetic field ⓘ |
| namedAfter |
Félix Savart
ⓘ
Jean-Baptiste Biot ⓘ |
| proportionalTo | electric current I ⓘ |
| relatedTo |
Ampère's law
ⓘ
linked to:
Ampère's force law
Coulomb's law ⓘ Maxwell's equations ⓘ |
| relates | steady electric current to magnetic field ⓘ |
| typeOf | integral law in electromagnetism ⓘ |
| usedIn |
computational electromagnetics
ⓘ
linked to:
finite element method
design of electromagnets ⓘ design of inductors ⓘ design of magnetic resonance imaging systems ⓘ magnetic field calculations in engineering ⓘ plasma physics ⓘ |
| usedToDerive |
magnetic field of a circular current loop
ⓘ
magnetic field of a current-carrying arc ⓘ magnetic field of a long straight wire ⓘ magnetic field of a solenoid ⓘ magnetic field of arbitrary current distributions ⓘ |
| usesSymbol |
B for magnetic field
ⓘ
I for electric current ⓘ dℓ for current element ⓘ r for field point position vector ⓘ r̂ for unit vector from source to field point ⓘ r′ for source point position vector ⓘ μ₀ for permeability of free space ⓘ |
| validIn | magnetostatic approximation ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Biot–Savart law Description of subject: The Biot–Savart law is a fundamental equation in electromagnetism that gives the magnetic field produced by a steady electric current by integrating contributions from each current element in space.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.