Electromagnetics

ELECTROMAGNETICS......Page 1
Electrical Engineering Textbook Series......Page 2
Preface......Page 6
Contents......Page 8
Table of Contents......Page 0
1.1 Notation, conv ntions, and symbology......Page 13
1.2.1 Historical perspective......Page 14
1.2.2 Formalization of field theory......Page 16
1.3 The sources of the electromagnetic field......Page 17
1.3.1 Macroscopic electromagnetics......Page 18
1.3.2 Impressed vs. secondary sources......Page 21
1.3.3 Surface and line source densities......Page 22
1.3.4 Charge conservation......Page 24
1.3.5 Magnetic charge......Page 29
1.4 Problems......Page 30
2.1 The postulate......Page 31
2.1.1 The Maxwell–Minkowski equations......Page 32
2.1.2 Connection to mechanics......Page 35
2.2 The well-posed nature of the postulate......Page 36
2.2.1 Uniqueness of solutions to Maxwell'sequations......Page 37
2.2.2 Constitutive relations......Page 39
2.3 Maxwell's equations in moving frames......Page 46
2.3.1 Field conversions under Galilean transformation......Page 47
2.3.2 Field conversions under Lorentz transformation......Page 50
2.4 The Maxwell–Boffi equations......Page 56
2.5 Large-scale form of Maxwell's equations......Page 60
2.5.1 Surface moving with constant velocity......Page 61
2.5.2 Moving, deforming surfaces......Page 67
2.5.3 Large-scale form of the Boffi equations......Page 68
2.6 The nature of the four field quantities......Page 70
2.7 Maxwell's equations with magnetic sources......Page 71
2.8.1 Boundary conditions across a stationary, thin source layer......Page 73
2.8.2 Boundary conditions  across a stationary layer of field discontinuity......Page 75
2.8.3 Boundary conditions at the surface of a perfect conductor......Page 79
2.8.5 Boundary conditions across a moving layer of field discontinuity......Page 80
2.9.1 Linearity......Page 81
2.9.2 Duality......Page 82
2.9.3 Reciprocity......Page 86
2.9.4 Similitude......Page 87
2.9.5 Conservation theorems......Page 89
2.10 The wave nature of the electromagnetic field......Page 100
2.10.1 Electromagnetic waves......Page 101
2.10.2 Wave equation for bianisotropic materials......Page 102
2.10.3 Wave equation in a conducting medium......Page 104
2.10.6 Transient uniform plane waves in a conducting medium......Page 105
2.10.7 Propagation of cylindrical waves in a lossless medium......Page 112
2.10.8 Propagation of spherical waves in a lossless medium......Page 116
2.10.9 Nonradiating sources......Page 119
2.11 Problems......Page 120
3.1 Static fields and steady currents......Page 124
3.1.1 Decoupling of the electric and magnetic fields......Page 125
3.1.2 Static field equilibrium and conductors......Page 126
3.1.3 Steady current......Page 128
3.2.1 The electrostatic potential and work......Page 130
3.2.2 Boundary conditions......Page 132
3.2.3 Uniqueness of the electrostatic field......Page 134
3.2.4 Poisson's and Laplace's equations......Page 135
3.2.5 Force and energy......Page 149
3.2.6 Multipole expansion......Page 153
3.2.7 Field produced by a permanently polarized body......Page 159
3.2.8 Potential of a dipole layer......Page 160
3.2.9 Behavior of electric charge density near a conducting edge......Page 162
3.2.10 Solution to Laplace's equation for bodies immersed in an impressed field......Page 164
3.3 Magnetostatics......Page 165
3.3.1 The magnetic vector potential......Page 168
3.3.2 Multipole expansion......Page 171
3.3.3 Boundary conditions for the magnetostatic field......Page 173
3.3.5 Integral solution for the vector potential......Page 175
3.3.6 Force and energy......Page 178
3.3.7 Magnetic field of a permanently magnetized body......Page 187
3.3.8 Bodies immersed in an impressed magnetic field:magnetostatic shielding......Page 189
3.4.3 Thomson's theorem......Page 191
3.4.4 Green's reciprocation theorem......Page 193
3.5 Problems......Page 194
4.1 Interpretation of the temporal transform......Page 200
4.2 The frequency-domain Maxwell equations......Page 201
4.3 Boundary conditions on the frequency-domain fields......Page 202
4.4 Constitutive relations in the frequency domain and the Kronig–Kramers relations......Page 203
4.4.1 The complex permittivity......Page 204
4.4.3 The Kronig –Kramers relations......Page 205
4.5 Dissipated and stored energy in a dispersive medium......Page 209
4.5.1 Dissipation in a dispersive material......Page 210
4.5.2 Energy stored in a dispersive material......Page 213
4.5.3 The energy theorem......Page 217
4.6.1 Complex permittivity of a non-magnetized plasma......Page 218
4.6.2 Complex dyadic permittivity of a magnetized plasma......Page 223
4.6.3 Simple models of dielectrics......Page 225
4.6.5 Permeability dyadic of a ferrite......Page 238
4.7 Monochromatic fields and the phasor domain......Page 243
4.7.1 The time-harmonic EM fields and constitutive relations......Page 244
4.7.2 The phasor fields and Maxwell's equations......Page 245
4.8 Poynting's theorem for time-harmonic fields......Page 246
4.8.1 General form of Poynting's theorem......Page 247
4.8.2 Poynting's theorem for nondispersive materials......Page 248
4.8.3 Lossless, lossy, and active media......Page 250
4.9 The complex Poynting theorem......Page 252
4.10.1 Uniqueness......Page 254
4.10.2 Reciprocity revisited......Page 257
4.10.3 Duality......Page 260
4.11.1 The frequency-domain wave equation......Page 263
4.11.2 Field relationships and the wave equation for two-dimensional fields......Page 264
4.11.3 Plane waves in a homogeneous, isotropic, lossy material......Page 267
4.11.4 Monochromatic plane waves in a lossy medium......Page 278
4.11.5 Plane waves in layered media......Page 288
4.11.6 Plane-wave propagation in an anisotropic ferrite medium......Page 309
4.11.7 Propagation of cylindrical waves......Page 312
4.11.8 Propagation of spherical waves in a conducting medium......Page 329
4.12 Interpretation of the spatial transform......Page 333
4.13 Spatial Fourier decomposition of two-dimensional fields......Page 335
4.13.1 Boundary value problems using the spatial Fourier representation......Page 340
4.14 Periodic fields and Floquet's theorem......Page 349
4.14.1 Floquet's theorem......Page 350
4.14.2 Examples of periodic systems......Page 351
4.15 Problems......Page 354
5.1.1 Planar field symmetry......Page 360
5.2 Solenoidal –lamellar decomposition......Page 365
5.2.1 Solution for potentials in an unbounded medium:the retarded potentials......Page 375
5.2.2 Solution for potential functions in a bounded medium......Page 385
5.3.1 Transverse –longitudinal decomposition in terms of fields......Page 387
5.4.1 TE –TM decomposition in terms of fields......Page 390
5.4.2 TE –TM decomposition in terms of Hertzian potentials......Page 391
5.4.3 Application:hollow-pipe waveguides......Page 393
5.4.4 TE –TM decomposition in spherical coordinates......Page 403
5.5 Problems......Page 412
6.1.1 The Stratton–Chu formula......Page 418
6.1.2 The Sommerfeld radiation condition......Page 422
6.1.3 Fields in the excluded region: the extinction theorem......Page 423
6.2 Fields in an unbounded medium......Page 424
6.2.1 The far-zone fields produced by sources in unbounded space......Page 425
6.3.1 The vector Huygens principle......Page 431
6.3.2 The Franz formula......Page 432
6.3.3 Love's equivalence principle......Page 433
6.3.4 The Schelkunoff equivalence principle......Page 435
6.3.5 Far-zone fields produced by equivalent sources......Page 436
6.4 Problems......Page 439
One-dimensional case......Page 440
Transforms of multi-variable functions......Page 444
A review of complexcontour integration......Page 446
Fourier transform solution of the 1-D wave equation......Page 450
Fourier transform solution of the 1-D homogeneous wave equation for dissipative media......Page 456
The 3-D Green ’s function for waves in dissipative media......Page 459
Fourier transform representation of the static Green ’s function......Page 461
Partial,total,and material derivatives......Page 464
The Helmholtz and Reynolds transport theorems......Page 466
A.3 Dyadic analysis......Page 468
Sturm –Liouville problems and eigenvalues......Page 474
Separation of variables......Page 482
Integral theorems......Page 503
Derivative identities......Page 505
Identities involving the plane-wave function......Page 506
Identities involving the transverse/longitudinal decomposition......Page 507
Some ourier transform pairs......Page 508
Rectangular coordinate system......Page 510
Cylindrical coordinate system......Page 512
Spherical coordinate system......Page 514
Differential equations......Page 518
Orthogonality relationships......Page 519
Functional relationships......Page 520
Large argument approximations......Page 521
Integral representations......Page 522
Summation formulas......Page 523
Notation......Page 524
Specific examples......Page 525
Functional relationships......Page 526
Summations......Page 527
Differential equation......Page 528
Addition formulas......Page 529
Series expansion of a function......Page 530
References......Page 531