Ampère–Maxwell law
E32547
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.
Observed surface forms (2)
| Surface form | Occurrences |
|---|---|
| Ampère's circuital law | 2 |
| Maxwell displacement current | 1 |
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
Maxwell equation
ⓘ
electromagnetic law ⓘ physical law ⓘ |
| applicableIn |
material media
ⓘ
vacuum ⓘ |
| category | laws of electromagnetism ⓘ |
| containsConstant |
vacuum permeability μ₀
ⓘ
vacuum permittivity ε₀ ⓘ |
| containsTerm |
curl of magnetic field
ⓘ
current density ⓘ time derivative of electric field ⓘ |
| corrects | original Ampère's law for time-varying fields ⓘ |
| dimension | vector equation ⓘ |
| enables | prediction of electromagnetic waves ⓘ |
| ensures |
charge conservation consistency
ⓘ
continuity equation compatibility ⓘ |
| expressedIn |
differential form
ⓘ
integral form ⓘ |
| field | electromagnetism ⓘ |
| generalizes |
Ampère–Maxwell law
self-linksurface differs
ⓘ
surface form:
Ampère's circuital law
|
| hasComponent |
conduction current term
ⓘ
displacement current term ⓘ |
| historicalRole | completion of Maxwell's equations ⓘ |
| implies | existence of electromagnetic waves in vacuum ⓘ |
| introducedBy | James Clerk Maxwell ⓘ |
| introducesConcept | displacement current density ⓘ |
| mathematicalOperator | curl operator ∇× ⓘ |
| namedAfter |
André-Marie Ampère
ⓘ
James Clerk Maxwell ⓘ |
| partOf | Maxwell's equations ⓘ |
| relatedConcept |
Ampère–Maxwell law
self-linksurface differs
ⓘ
surface form:
Maxwell displacement current
continuity equation for electric charge ⓘ electromagnetic wave propagation ⓘ |
| relates |
changing electric field
ⓘ
displacement current ⓘ electric current ⓘ magnetic field ⓘ |
| relatesQuantity |
current density J
ⓘ
electric field E ⓘ magnetic field B ⓘ |
| standardFormIntegral | ∮_C B · dl = μ₀I_enclosed + μ₀ε₀ dΦ_E/dt ⓘ |
| standardFormSI | ∇ × B = μ₀J + μ₀ε₀ ∂E/∂t ⓘ |
| usedIn |
analysis of capacitors with time-varying fields
ⓘ
antenna theory ⓘ derivation of wave equation for electromagnetic fields ⓘ electromagnetic field theory ⓘ electromagnetic radiation analysis ⓘ |
| validIn | classical electromagnetism ⓘ |
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Ampère's circuital law
this entity surface form:
Ampère's circuital law
this entity surface form:
Maxwell displacement current