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.
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
equation in electromagnetism
ⓘ
physical law ⓘ |
| analogousTo | Coulomb's law for electric fields NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ |
| 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
NERFINISHED
ⓘ
Jean-Baptiste Biot NERFINISHED ⓘ |
| proportionalTo | electric current I ⓘ |
| relatedTo |
Ampère's law
NERFINISHED
ⓘ
Coulomb's law NERFINISHED ⓘ Maxwell's equations NERFINISHED ⓘ |
| relates | steady electric current to magnetic field ⓘ |
| typeOf | integral law in electromagnetism ⓘ |
| usedIn |
computational electromagnetics
NERFINISHED
ⓘ
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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.