Electromagnetics

Title:

Electromagnetics

Personal Author:

Rothwell, Edward J.

Series:

Electrical engineering textbook series

Publication Information:

Boca Raton, Fla. : CRC Press, 2001

ISBN:

9780849313974

General Note:

Also available in online version from EngnetBase

Subject Term:

Electromagnetic theory

Added Author:

Cloud, Michael J.

Electronic Access:

Online access via EngnetBase

DSP_RESTRICTION_NOTE:

EngnetBase is open access to UTM community only

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000004565598	QC670 R69 2001	Open Access Book	Book	Searching... Unknown

Between a first undergraduate course in electromagnetism (EM) and the advanced graduate course lies a middle ground that is essential to engineering students yet virtually ignored by most curricula. It is the transition from the basic, more superficial treatments to the sharply focused graduate studies that solidifies students' understanding of EM fundamentals before they move on to a specialized area of research. And it is here that academia-and practitioners still uneasy about the fundamentals-have lacked the appropriate "intermediate" text.

Electromagnetics provides that transition. Emphasizing concepts over problem-solving techniques, it focuses on the topics most important to EM research and those most troublesome to beginning graduate students. In Part I, the authors cover the required mathematics background and introduce the primary physical principles. From a well-posed postulate, Part II builds a complete description of the EM field in free space, and Part III completes the study by investigating the behavior of the EM field in a variety of materials. Stressing both a physical understanding and a detailed mathematical description of each topic, this text provides an account of EM theory that is in-depth, lucid, and accessible.

Highly engaging prose, clear, concise explanations, and numerous examples relating concepts to modern engineering applications create a comfortable atmosphere that enhances the reader's grasp of the material. Electromagnetics thus builds a foundation that allows readers to proceed with confidence to advanced EM studies, research, and applications.

Preface	p. vii
1 Introductory concepts	p. 1
1.1 Notation, conventions, and symbology	p. 1
1.2 The field concept of electromagnetics	p. 2
1.2.1 Historical perspective	p. 2
1.2.2 Formalization of field theory	p. 4
1.3 The sources of the electromagnetic field	p. 5
1.3.1 Macroscopic electromagnetics	p. 6
1.3.2 Impressed vs. secondary sources	p. 9
1.3.3 Surface and line source densities	p. 10
1.3.4 Charge conservation	p. 12
1.3.5 Magnetic charge	p. 17
1.4 Problems	p. 18
2 Maxwell's theory of electromagnetism	p. 19
2.1 The postulate	p. 19
2.1.1 The Maxwell-Minkowski equations	p. 20
2.1.2 Connection to mechanics	p. 23
2.2 The well-posed nature of the postulate	p. 24
2.2.1 Uniqueness of solutions to Maxwell's equations	p. 25
2.2.2 Constitutive relations	p. 27
2.3 Maxwell's equations in moving frames	p. 34
2.3.1 Field conversions under Galilean transformation	p. 35
2.3.2 Field conversions under Lorentz transformation	p. 38
2.4 The Maxwell-Boffi equations	p. 44
2.5 Large-scale form of Maxwell's equations	p. 48
2.5.1 Surface moving with constant velocity	p. 49
2.5.2 Moving, deforming surfaces	p. 55
2.5.3 Large-scale form of the Boffi equations	p. 56
2.6 The nature of the four field quantities	p. 58
2.7 Maxwell's equations with magnetic sources	p. 59
2.8 Boundary (jump) conditions	p. 61
2.8.1 Boundary conditions across a stationary, thin source layer	p. 61
2.8.2 Boundary conditions across a stationary layer of field discontinuity	p. 63
2.8.3 Boundary conditions at the surface of a perfect conductor	p. 67
2.8.4 Boundary conditions across a stationary layer of field discontinuity using equivalent sources	p. 68
2.8.5 Boundary conditions across a moving layer of field discontinuity	p. 68
2.9 Fundamental theorems	p. 69
2.9.1 Linearity	p. 69
2.9.2 Duality	p. 70
2.9.3 Reciprocity	p. 74
2.9.4 Similitude	p. 75
2.9.5 Conservation theorems	p. 77
2.10 The wave nature of the electromagnetic field	p. 88
2.10.1 Electromagnetic waves	p. 89
2.10.2 Wave equation for bianisotropic materials	p. 90
2.10.3 Wave equation in a conducting medium	p. 92
2.10.4 Scalar wave equation for a conducting medium	p. 93
2.10.5 Fields determined by Maxwell's equations vs. fields determined by the wave equation	p. 93
2.10.6 Transient uniform plane waves in a conducting medium	p. 93
2.10.7 Propagation of cylindrical waves in a lossless medium	p. 100
2.10.8 Propagation of spherical waves in a lossless medium	p. 104
2.10.9 Nonradiating sources	p. 107
2.11 Problems	p. 108
3 The static electromagnetic field	p. 113
3.1 Static fields and steady currents	p. 113
3.1.1 Decoupling of the electric and magnetic fields	p. 114
3.1.2 Static field equilibrium and conductors	p. 115
3.1.3 Steady current	p. 117
3.2 Electrostatics	p. 119
3.2.1 The electrostatic potential and work	p. 119
3.2.2 Boundary conditions	p. 121
3.2.3 Uniqueness of the electrostatic field	p. 123
3.2.4 Poisson's and Laplace's equations	p. 124
3.2.5 Force and energy	p. 138
3.2.6 Multipole expansion	p. 142
3.2.7 Field produced by a permanently polarized body	p. 148
3.2.8 Potential of a dipole layer	p. 149
3.2.9 Behavior of electric charge density near a conducting edge	p. 151
3.2.10 Solution to Laplace's equation for bodies immersed in an impressed field	p. 153
3.3 Magnetostatics	p. 154
3.3.1 The magnetic vector potential	p. 157
3.3.2 Multipole expansion	p. 160
3.3.3 Boundary conditions for the magnetostatic field	p. 162
3.3.4 Uniqueness of the magnetostatic field	p. 164
3.3.5 Integral solution for the vector potential	p. 164
3.3.6 Force and energy	p. 167
3.3.7 Magnetic field of a permanently magnetized body	p. 176
3.3.8 Bodies immersed in an impressed magnetic field: magnetostatic shielding	p. 178
3.4 Static field theorems	p. 180
3.4.1 Mean value theorem of electrostatics	p. 180
3.4.2 Earnshaw's theorem	p. 180
3.4.3 Thomson's theorem	p. 180
3.4.4 Green's reciprocation theorem	p. 182
3.5 Problems	p. 183
4 Temporal and spatial frequency domain representation	p. 189
4.1 Interpretation of the temporal transform	p. 189
4.2 The frequency-domain Maxwell equations	p. 190
4.3 Boundary conditions on the frequency-domain fields	p. 191
4.4 The constitutive and Kronig-Kramers relations	p. 192
4.4.1 The complex permittivity	p. 193
4.4.2 High and low frequency behavior of constitutive parameters	p. 194
4.4.3 The Kronig-Kramers relations	p. 194
4.5 Dissipated and stored energy in a dispersive medium	p. 198
4.5.1 Dissipation in a dispersive material	p. 199
4.5.2 Energy stored in a dispersive material	p. 202
4.5.3 The energy theorem	p. 206
4.6 Some simple models for constitutive parameters	p. 207
4.6.1 Complex permittivity of a non-magnetized plasma	p. 207
4.6.2 Complex dyadic permittivity of a magnetized plasma	p. 212
4.6.3 Simple models of dielectrics	p. 214
4.6.4 Permittivity and conductivity of a conductor	p. 227
4.6.5 Permeability dyadic of a ferrite	p. 227
4.7 Monochromatic fields and the phasor domain	p. 232
4.7.1 The time-harmonic EM fields and constitutive relations	p. 233
4.7.2 The phasor fields and Maxwell's equations	p. 234
4.7.3 Boundary conditions on the phasor fields	p. 235
4.8 Poynting's theorem for time-harmonic fields	p. 235
4.8.1 General form of Poynting's theorem	p. 236
4.8.2 Poynting's theorem for nondispersive materials	p. 237
4.8.3 Lossless, lossy, and active media	p. 239
4.9 The complex Poynting theorem	p. 241
4.9.1 Boundary condition for the time-average Poynting vector	p. 243
4.10 Fundamental theorems for time-harmonic fields	p. 243
4.10.1 Uniqueness	p. 243
4.10.2 Reciprocity revisited	p. 246
4.10.3 Duality	p. 249
4.11 The wave nature of the time-harmonic EM field	p. 252
4.11.1 The frequency-domain wave equation	p. 252
4.11.2 Field relationships and the wave equation for two-dimensional fields	p. 253
4.11.3 Plane waves in a homogeneous, isotropic, lossy material	p. 256
4.11.4 Monochromatic plane waves in a lossy medium	p. 267
4.11.5 Plane waves in layered media	p. 277
4.11.6 Plane-wave propagation in an anisotropic ferrite medium	p. 298
4.11.7 Propagation of cylindrical waves	p. 301
4.11.8 Propagation of spherical waves in a conducting medium	p. 318
4.11.9 Nonradiating sources	p. 322
4.12 Interpretation of the spatial transform	p. 322
4.13 Spatial Fourier decomposition	p. 324
4.13.1 Boundary value problems using the spatial Fourier representation	p. 329
4.14 Periodic fields and Floquet's theorem	p. 338
4.14.1 Floquet's theorem	p. 339
4.14.2 Examples of periodic systems	p. 340
4.15 Problems	p. 343
5 Field decompositions and the EM potentials	p. 349
5.1 Spatial symmetry decompositions	p. 349
5.1.1 Planar field symmetry	p. 349
5.2 Solenoidal-lamellar decomposition	p. 354
5.2.1 Solution for potentials in an unbounded medium: the retarded potentials	p. 364
5.2.2 Solution for potential functions in a bounded medium	p. 374
5.3 Transverse-longitudinal decomposition	p. 376
5.3.1 Transverse-longitudinal decomposition in terms of fields	p. 376
5.4 TE-TM decomposition	p. 379
5.4.1 TE-TM decomposition in terms of fields	p. 379
5.4.2 TE-TM decomposition in terms of Hertzian potentials	p. 380
5.4.3 Application: hollow-pipe waveguides	p. 382
5.4.4 TE-TM decomposition in spherical coordinates	p. 392
5.5 Problems	p. 401
6 Integral solutions of Maxwell's equations	p. 407
6.1 Vector Kirchoff solution	p. 407
6.1.1 The Stratton-Chu formula	p. 407
6.1.2 The Sommerfeld radiation condition	p. 411
6.1.3 Fields in the excluded region: the extinction theorem	p. 412
6.2 Fields in an unbounded medium	p. 413
6.2.1 The far-zone fields produced by sources in unbounded space	p. 414
6.3 Fields in a bounded, source-free region	p. 420
6.3.1 The vector Huygens principle	p. 420
6.3.2 The Franz formula	p. 421
6.3.3 Love's equivalence principle	p. 422
6.3.4 The Schelkunoff equivalence principle	p. 424
6.3.5 Far-zone fields produced by equivalent sources	p. 425
6.4 Problems	p. 428
A Mathematical appendix	p. 429
A.1 The Fourier transform	p. 429
A.2 Vector transport theorems	p. 453
A.3 Dyadic analysis	p. 457
A.4 Boundary value problems	p. 463
B Useful identities	p. 493
C Some Fourier transform pairs	p. 499
D Coordinate systems	p. 501
E Properties of special functions	p. 509
E.1 Bessel functions	p. 509
E.2 Legendre functions	p. 515
E.3 Spherical harmonics	p. 519
References	p. 523

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