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Induction Currents from CircularCoils
Introduction
Atime- phenomenonbya time-harmonicfieldsimulationas wellasatransientanalysis,whichprovidesastudyoftheeddycurrentsresultingfromswitchingonthesource.
Twocurrent- byair, -harmoniccaseshowstheskineffect,thatis,thatthecurrentdensityishighclosetothesurfaceanddecreasesrapidlyinsidetheconductor.
ModelDefinition
EQUATION
Tosolvetheproblem,useaquasi-staticequationforthemagneticpotentialA:
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σ-∂--A----+∇×(μ–1μ–1∇×A) = σVcoi-l
∂t 0 r
2πr
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Hereμ0isthepermeabilityofvacuum,μrthe relativepermeability,σtheelectricconductivity,andVcoilthevoltageoveroneturnin -harmoniccasetheequationreducesto
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–1 –1
V
coil
= -----------
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jωσA+∇×(μ0 μr
∇×A)
σ2πr
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FORCES
ThetotalelectromagneticforceactingonregionofspaceΩ canbeobtainedbyintegratingMaxwell’sstresstensor onthedelimitingboundary ∂Ω:
F= ò TndS
∂Ω
TheForceCalculationfeatureautomaticallyperformstheintegralalongtheboundariesofthedesiredregion,.
ResultsandDiscussion
Inthetime-harmonicregime,thevaryingmagneticfieldinduceselectricalcurrentsin ,inturn,actassourcesofanopposingmagneticfield“shielding”,theregioninwhichelectricalcurrentsaregeneratedisconfinedinproximityofthesurfacean