Eddy Currents

About the Authors ix
 
Preface x
 
Part I Theory 1
 
1 Basic Principles of Eddy Currents 3
 
1.1 Introduction 3
 
1.2 Faraday's Law and Lenz's Law 5
 
1.3 Proximity Effect 8
 
1.4 Resistance and Reactance Limited Eddy Currents 11
 
1.5 Electromotive Force (emf) and Potential Difference 14
 
1.6 Waves, Diffusion, and the Magneto-Quasi-static Approximation 22
 
1.7 Skin Depth or Depth of Penetration 27
 
1.8 Diffusion, Heat Transfer, and Eddy Currents 30
 
1.9 The Diffusion Equation and RandomWalks 32
 
1.10 Transient Magnetic Diffusion 34
 
1.11 Coupled Circuit Models for Eddy Currents 39
 
1.12 Summary 43
 
2 Conductors with Rectangular Cross Sections 45
 
2.1 Finite Plate: Resistance Limited 45
 
2.2 Infinite Plate: Reactance Limited 48
 
2.3 Finite Plate: Reactance Limited 53
 
2.4 Superposition of Eddy Losses in a Conductor 58
 
2.5 Discussion of Losses in Rectangular Plates 59
 
2.6 Eddy Currents in a Nonlinear Plate 68
 
2.7 Plate with Hysteresis and Complex Permeability 80
 
2.8 Conducting Plates with Sinusoidal Space Variation of Field 83
 
2.9 Eddy Currents in Multi-Layered Plate Geometries 94
 
2.10 Thin Wire Carrying Current Above Conducting Plates 100
 
2.11 Eddy Currents in Materials with Anisotropic Permeability 112
 
2.12 Isolated Rectangular Conductor with Axial Current Applied 115
 
2.13 Transient Diffusion Into a Solid Conducting Block 118
 
2.14 Eddy Current Modes in a Rectangular Core 125
 
2.15 Summary 129
 
3 Conductors with Circular Cross Sections 131
 
3.1 Axial Current in a Conductor with Circular Cross Section: Reactance-Limited Case 131
 
3.2 Axial Current in Composite Circular Conductors 136
 
3.3 Circular Conductor with Applied Axial Flux: Resistance-Limited Case 144
 
3.4 Circular Conductor

Sheppard J. Salon, PhD, is Professor Emeritus in the Department of Electrical, Computer and Systems Engineering at Rensselaer Polytechnic Institute in Troy, New York, USA, and a founder of the Magsoft Corporation. He has published on many electrical engineering subjects and his awards and honors include an IEEE Life Fellowship and the IEEE 2004 Nicola Tesla Award.
 
M. V. K. Chari, PhD, now retired, was a Research Professor at Rensselaer Polytechnic Institute in Troy, New York, USA. He is a former Technical Leader at General Electric, an IEEE Life Fellow, and recipient of the 1993 Nicola Tesla Award. He has published extensively on electrical engineering subjects.
 
Lale T. Ergene, PhD, is a Full Professor in the Electrical Engineering Department at Istanbul Technical University, Turkey. She was an adjunct professor at Rensselaer Polytechnic Institute in Troy, New York, USA and worked at MAGSOFT Corporation as a consulting engineer. She is IEEE Senior Member and advisory board member of the Scientific and Technological Research Council of Turkey. She has published widely on electrical engineering subjects.
 
David Burow, PhD, is Owner and Head Programmer at Genfo, Inc., a company that provides custom programming for Macintosh, Windows, and Linux operating systems. He was a Postdoctoral Researcher at Rensselaer Polytechnic Institute and has published several papers on electrical engineering subjects.
 
Mark DeBortoli, PhD, received a doctoral degree at Rensselaer Polytechnic Institute. He has over 30 years of industrial experience and is currently an engineering consultant.