Gauss's law for magnetism
E31558
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.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
Maxwell equation
ⓘ
law of electromagnetism ⓘ physical law ⓘ |
| appliesTo | closed surfaces ⓘ |
| approximationLevel | classical (non-quantum) description ⓘ |
| assumes | absence of magnetic charge density ⓘ |
| componentOf | set of four Maxwell equations ⓘ |
| consequence |
magnetic field is solenoidal
ⓘ
magnetic field lines have no beginning or end ⓘ |
| contrastsWith |
Gauss’s law
ⓘ
surface form:
Gauss's law for electricity
|
| coordinateForm | ∂B_x/∂x + ∂B_y/∂y + ∂B_z/∂z = 0 ⓘ |
| expressedIn | Maxwell's equations ⓘ |
| expresses | divergence-free nature of the magnetic field ⓘ |
| field |
classical electrodynamics
ⓘ
electromagnetism ⓘ |
| formulatedIn |
differential form
ⓘ
integral form ⓘ |
| holdsIn |
linear media
ⓘ
nonlinear media ⓘ vacuum ⓘ |
| implies |
magnetic field lines form closed loops
ⓘ
magnetic monopoles do not exist in classical electromagnetism ⓘ |
| involvesConcept |
closed surface integral
ⓘ
magnetic flux conservation ⓘ |
| involvesOperator | divergence operator ⓘ |
| isIntegralFormOf | ∇ · B = 0 ⓘ |
| isLocalFormOf | ∮_S B · dA = 0 ⓘ |
| mathematicalForm |
∇ · B = 0
ⓘ
∮_S B · dA = 0 ⓘ |
| namedAfter | Carl Friedrich Gauss ⓘ |
| quantityDescribed |
magnetic field
ⓘ
magnetic flux ⓘ |
| relatedTo |
Ampère–Maxwell law
ⓘ
Faraday's law of induction ⓘ Faraday's law of induction ⓘ
surface form:
Maxwell–Faraday equation
|
| representedIn | tensor form of electromagnetism ⓘ |
| states | the net magnetic flux through any closed surface is zero ⓘ |
| status | empirically well supported ⓘ |
| testedBy | searches for magnetic monopoles ⓘ |
| usedIn |
electromagnetic theory
ⓘ
magnetohydrodynamics ⓘ magnetostatics ⓘ plasma physics ⓘ |
| usesSymbol |
B
ⓘ
dA ⓘ ∇ ⓘ |
| validIn | special relativity ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.