Inductance: Loop and Partial

395 Pages·2009·1.798 MB·English

by  Clayton R. Paul

INDUCTANCE

INDUCTANCE
Loop and Partial
CLAYTONR.PAUL
ProfessorofElectricalandComputerEngineering
MercerUniversity
Macon,Georgia
and
EmeritusProfessorofElectricalEngineering
UniversityofKentucky
Lexington,Kentucky
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Paul,ClaytonR.
Inductance:loopandpartial/ClaytonR.Paul.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN978-0-470-46188-4
1. Inductance. 2. Inductioncoils. I. Title.
QC638.P382010
621.37’42–dc22 2009031434
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
ThisbookisdedicatedtothememoryofmyFatherandmyMother
OscarPaul
and
LouisePaul

CONTENTS
Preface xi
1 Introduction 1
1.1 HistoricalBackground, 1
1.2 FundamentalConceptsofLumpedCircuits, 2
1.3 OutlineoftheBook, 7
1.4 “Loop”Inductancevs.“Partial”Inductance, 8
2 MagneticFieldsofDCCurrents(SteadyFlowofCharge) 13
2.1 MagneticFieldVectorsandPropertiesofMaterials, 13
2.2 Gauss’sLawfortheMagneticField
andtheSurfaceIntegral, 15
2.3 TheBiot–SavartLaw, 19
2.4 Ampe`re’sLawandtheLineIntegral, 34
2.5 VectorMagneticPotential, 47
2.5.1 Leibnitz’sRule:DifferentiateBefore
YouIntegrate, 67
2.6 DeterminingtheInductanceofaCurrentLoop:
APreliminaryDiscussion, 71
2.7 EnergyStoredintheMagneticField, 79
2.8 TheMethodofImages, 80
2.9 Steady(DC)CurrentsMustFormClosedLoops, 83
vii
viii CONTENTS
3 FieldsofTime-VaryingCurrents
(AcceleratedCharge) 87
3.1 Faraday’sFundamentalLawofInduction, 88
3.2 Ampe`re’sLawandDisplacementCurrent, 98
3.3 Waves,Wavelength,TimeDelay,
andElectricalDimensions, 102
3.4 HowCanResultsDerivedUsingStatic(DC)Voltages
andCurrentsbeUsedinProblemsWheretheVoltages
andCurrentsareVaryingwithTime?, 105
3.5 VectorMagneticPotentialforTime-VaryingCurrents, 107
3.6 ConservationofEnergyandPoynting’sTheorem, 111
3.7 InductanceofaConductingLoop, 113
4 TheConceptof“Loop”Inductance 117
4.1 SelfInductanceofaCurrentLoopfromFaraday’sLaw
ofInduction, 117
4.1.1 RectangularLoop, 121
4.1.2 CircularLoop, 126
4.1.3 CoaxialCable, 130
4.2 TheConceptofFluxLinkagesforMultiturnLoops, 133
4.2.1 Solenoid, 134
4.2.2 Toroid, 137
4.3 LoopInductanceUsingtheVectorMagneticPotential, 139
4.3.1 RectangularLoop, 141
4.3.2 CircularLoop, 144
4.4 NeumannIntegralforSelfandMutualInductancesBetween
CurrentLoops, 145
4.4.1 MutualInductanceBetweenTwoCircularLoops, 147
4.4.2 SelfInductanceoftheRectangularLoop, 150
4.4.3 SelfInductanceoftheCircularLoop, 153
4.5 InternalInductancevs.ExternalInductance, 155
4.6 UseofFilamentaryCurrentsandCurrentRedistributionDue
totheProximityEffect, 158
4.6.1 Two-WireTransmissionLine, 159
4.6.2 OneWireAboveaGroundPlane, 161
4.7 EnergyStorageMethodforComputing
LoopInductance, 163
4.7.1 InternalInductanceofaWire, 164
4.7.2 Two-WireTransmissionLine, 165
4.7.3 CoaxialCable, 165