Electromagnetic Fields: Waves and Numerical Methods

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ISBN: 9781586030643 | 1586030647
Cover: Hardcover
Copyright: 1/1/2001

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This book gives a complete overview of the classical electromagnetic theory, together with detailed insight in modern numerical methods for analysis of the problems in electromagnetics. Classical electromagnetic theory was developed in the 19th century, but due to the wide range of applications from electrical apparatus such as motors or heaters to telecommunications this subject is still very interesting. This book explains basic postulates and laws of the theory and its specialization to static and time-dependent problems. Special attention is given to utilization of computers in application of the modern numerical methods to solution of electromagnetic field problems.

The Electromagnetic Field

(46)

A Presentation of An Electromagnetic Field

(1)

Definitions of the fields E and B

(1)

Field Sources: Charge and Currents

(9)

Microscopic and macroscopic theory

(1)

Charge and current densities

(2)

Continuity equation

(1)

Singular source densities

(1)

Surface charge density and surface current density

(1)

Densities of a line charge and line current

(1)

Point sources

(1)

Discontinuities in a field

(1)

Field discontinuities caused by the surface density of a scalar source

(1)

Field Discontinuities caused by the surface density of a vector source

(1)

Maxwell's Equations in a Vacuum

(6)

Maxwell's equations in differential form

(1)

Maxwell's equations in integral form

(2)

An electromagnetic field in materials

(21)

A macroscopic model of a conductive material

(1)

Density of a conductive current in a material. Ohm's law

(1)

A conductor in an electric field

(2)

Polarization of materials. The vector of polarization P

(2)

Dielectric in an electric field

(2)

Magnetization of materials

(2)

A model of amperian currents in a magnetic material

(1)

A model of magnetic charge and current

(2)

Field vectors D and H. Electric and magnetic fluxes

(3)

Materials and constitutive relationships

(1)

Conductors

(1)

Insulators

(1)

Magnetic materials

(1)

Hysteresis

(1)

Ferromagnetic materials

(1)

Permanent magnets

(1)

Maxwell's Equations for fields in a material

(8)

Maxwell's equations for the model using amperian current

(1)

Equations

(1)

Boundary conditions

(2)

Maxwell's equations for a model with magnetic charge

(1)

Equations

(1)

Boundary conditions

(1)

Maxwell's equations for field vectors E, B, D and H

(2)

Problems

(1)

Electromagnetic potentials

(26)

Vector and scalar potential functions

(9)

Potentials and antipotentials in a dielectric without sources

(1)

Vector and scalar potentials

(1)

Wave equations

(1)

Antipotentials

(1)

Potentials in a conductive source-free material

(2)

Potentials and antipotentials of a given distribution of independent sources

(1)

Conductive material

(1)

Non-conductive material

(1)

Static charge and currents

(1)

Magnetic charge and currents

(1)

Gauge Transforms

(5)

The Lorentz gauge

(1)

Coulomb's gauge

(1)

Non-conductive material

(1)

Conductive material

(1)

A field with independent sources

(2)

Hertz potentials

(3)

Integral representation

(5)

The scalar potential of a point charge

(1)

Potentials of a time dependent distribution of space charge in an unbounded space

(2)

Retarded potentials in an unbounded space

(1)

Wave Equations and Integrals of Potentials

(4)

Problems

(1)

Energy and Forces In an Electromagnetic Fields

(28)

The Influence of an Electromagnetic Field on Moving Charges

(3)

Forces on charges in motion

(1)

Energy and power delivered to charges in motion

(1)

Electromagnetic energy

(7)

The conservation of electromagnetic energy. Poynting's theorem

(1)

Poynting's theorem in differential form

(1)

Poynting's theorem in an integral form

(1)

Conservation of electromagnetic energy in a vacuum

(2)

Stored electromagnetic energy in a cacuum

(2)

The flow of electromagnetic energy. Poynting's vector

(1)

A Material In An Electromagnetic Field

(8)

Electromagnetic energy absorbed in a material

(2)

Poynting's theorem in a material

(1)

Energy of polarization and electric energy

(3)

Energy of magnetization and magnetic energy

(1)

Poynting's theorem and electric and magnetic energy in materials

(1)

Volume Forces and Surface Stresses

(10)

Surface stresses in free space

(2)

Maxwell's stress tensor

(1)

The vector of electromagnetic stress

(2)

Forces and surface stresses in materials

(1)

Surface stresses in static fields at the boundary between two materials

(3)

Problems

100

(1)

A Static Electric Field

101

(50)

Equations of a Static Electric Field

101

(2)

Scalar electric potential

102

(1)

Visual Presentation of a Static Electric Field

103

(1)

Energy Stored in a Static Electric Field

104

(3)

Energy-based determination of forces in a static electric field

106

(1)

Capacitance

107

(3)

Capacitance of a condenser

107

(1)

A system of conductors and partial capacitances

108

(2)

The Solution of Static Electric Fields

110

(4)

The superposition of solutions of Poisson's Equation

111

(1)

The uniqueness of solutions of Poisson's equation

111

(2)

Integral of Poisson's equation and Green's functions

113

(1)

The Solution of Laplaces's Equation by a separation of Variables

114

(8)

Cartesian coordinate system

114

(3)

Cylindrical coordinate system

117

(3)

A spherical coordinate system

120

(2)

A Given Distribution of Charge in an Unbounded Space

122

(11)

A group of point charges

122

(4)

Line charges

126

(3)

Surface charge

129

(2)

Volume charge and a multipole expansion

131

(2)

Distribution of Charge in a Bounded Space and the Method of Images

133

(18)

Green's functions of plane metal boundaries

133

(1)

A point charge in front of a conductive plane

133

(1)

A point charge in a conductive angle

134

(1)

A line charge in front of a conductive plane

135

(3)

Green's functions of a plane dielectric boundary

138

(1)

A point charge in front of a plane boundary between dielectrics

138

(3)

Green's functions of a cylindrical boundary

141

(1)

A conductive cylindrical boundary

141

(3)

A dielectric cylindrical boundary

144

(2)

Green's function of a conductive spherical boundary

146

(3)

Problems

149

(2)

A Static Current Field in a Conductor

151

(6)

The field of Charge in uniform motion

151

(1)

Equations of a current Field and Field Analogies

152

(2)

Solution of a Current Field by the Method of Images

154

(3)

Problems

156

(1)

A Static Magnetic Field

157

(26)

Equations of a Static Magnetic Field

157

(1)

Potentials in a Static Magnetic Field

158

(1)

Magnetic vector potential

158

(1)

Antipotential

158

(1)

A Visual Presentation of a Static Magnetic Field

159

(1)

Energy stored in a Static Magnetic Field

160

(2)

Energy-based determination of forces in a static magnetic field

161

(1)

Inductances

162

(3)

Mutual inductance

163

(1)

The inductances of a systems of current loops

164

(1)

A magnetic Field in a Current-Free Region

165

(5)

The Field of Given Currents in an Unbounded Space

170

(10)

The field of line currents in an unbounded space

171

(4)

The field of a surface current

175

(2)

The field of volume currents and a multiple expansion

177

(3)

Given Currents in a Bounded Space and the Method of Images

180

(3)

Problems

182

(1)

A Quasi-Static Electromagnetic Field

183

(34)

Equations of a Quasi-Static Field

183

(3)

Validity of a quasi-static approximation

185

(1)

Field Equations in a Phasor Domain and Quasi-Static sinusoidal Fields

186

(3)

Sinusoidal time dependent fields and phasor notation

186

(1)

Electromagnetic Potentials in a phasor domain and a quasi-static approximation

187

(2)

Energy in a Quasi-static Field

189

(2)

Energy and power in a sinusoidal field

189

(2)

The Solution of a Quasi-Static Field in Conductors

191

(14)

Current Loops in a Quasi-Static Field

205

(12)

Steady current loops in a quasi-static field

206

(4)

Movement of a current loop in a quasi-static field electromagnetic induction

210

(2)

Electromechanical energy conversion

212

(4)

Problems

216

(1)

Electromagnetic Waves

217

(92)

Wave Equations of a Field in an Unbounded Source-Free Space

217

(3)

Wave equations

218

(1)

A separation of variables of the wave equation

218

(2)

A Plane Wave in an Unbounded Space

220

(16)

The separation of the Helmholtz equation

220

(1)

Equations of a plane wave

221

(5)

Plane waves sinusoidal in time

226

(4)

Plane waves sinusoidal in space

230

(2)

Fundamental characteristics of sinusoidal plane waves

232

(1)

Wave impedance

232

(1)

Energy flow

233

(1)

Polarization

234

(2)

The Propagation of Plane Waves

236

(19)

Waves in a dielectric

236

(1)

Travelling waves

237

(5)

Standing waves

242

(2)

Waves in a lossy conductive material

244

(3)

Classification of materials into insulators and conductors

247

(1)

Good insulators

248

(2)

Good conductors

250

(2)

The skin effect

252

(3)

Dispersion

255

(7)

Dispersion in dielectrics; the classical model for ε(ω)

256

(2)

Dispersion in metals

258

(2)

The group velocity of a signal

260

(2)

The Propagation of a Sinusoidal plane wave in Half-Bounded Regions

262

(12)

Reflection and refraction at a plane boundary

263

(1)

The laws of reflection and refraction

263

(2)

Fresnel formulae and the influence of polarization

265

(5)

The boundary between two dielectrics

270

(1)

Transmission of a wave into a lossy material

271

(3)

Propagation of Guided Plane Waves

274

(23)

Transmission lines

275

(7)

A terminated transmission line

282

(2)

Waveguides

284

(6)

Modes in a rectangular waveguide

290

(4)

Resonant cavities

294

(3)

Electromagnetic Wave Radiation

297

(12)

Electric Dipole radiation

297

(6)

The radiation field of a linear conductor

303

(5)

Problems

308

(1)

The Finite Element Method

309

(50)

A Definition of Fem

309

(5)

The integral form, and its approximation

311

(1)

A functional us an integral form

311

(1)

Weighted residual method

312

(2)

Two-dimensional static fields

314

(35)

An integral form equivalent to poisson's equation

314

(2)

Application of FEM to the integral form equivalent to Poisson's equation

316

(1)

An approximation of the geometry of the problem's domain

317

(4)

Organization of data on subdivision into elements

321

(1)

An approximation of the function on the element

322

(3)

Element integral forms of linear triangular elements used in solving Poisson's equation

325

(3)

Assembly of a system of equations

328

(1)

The algorithm for the assembly of the system

329

(1)

The solution of systems of linear algebraic equations in FEM

330

(1)

Triangularization

330

(1)

Back-substitution

331

(6)

Organization of data on the equation system

337

(4)

Calculation of electric and magnetic field strength

341

(1)

Calculation of the electric field vectors E and D

342

(1)

Calculation of the magnetic field vectors B and H

343

(1)

Visual representation of results of calculation by lines of constant potential

343

(1)

Calculation of equipotential lines

344

(1)

An example of calculation

345

(4)

Non-Linear Problems

349

(4)

A Quasi-static Field

353

(6)

Sinusoidal fields

353

(2)

Non-sinusoidal fields

355

(3)

Problems

358

(1)

The Method of Moments

359

(30)

Definition of Mom

359

(2)

Three-Dimensional Static electric Fields

361

(4)

An integral formulation of the problem

361

(1)

Application of MOM

362

(3)

Scattering of electromagnetic Waves

365

(13)

Integral form of the equations

366

(1)

TM field

366

(2)

TE field

368

(3)

Solution of a scattering problem by MOM

371

(1)

Scattering in a TM field

371

(4)

Scattering in a TE field

375

(3)

Thin-wire structures

378

(11)

Equivalent Sources

378

(1)

The integral formulation of scattering problems involving thin wires

379

(2)

Models of excitation for radiation sources

381

(2)

The solution of Pocklington's equation by the application of MOM

383

(3)

Far radiation field

386

(2)

Problems

388

(1)

APPENDIX A: DIRACδ-FUNCTION

389

(1)

APPENDIX B: VECTOR CALCULUS

390

(4)

B.1 Vector multiplication

390

(1)

B.2 Differential relationships

391

(2)

B.3 Integral relationships

393

(1)

APPENDIX C: COORDINATE SYSTEMS

394

(4)

C.1 A Cartesian coordinate system

394

(1)

C.2 A Cylindrical coordinate system

395

(1)

C.3 A Spherical coordinate system

396

(2)

APPENDIX D: BESSEL'S DIFFERENTIAL EQUATION

398

(4)

APPENDIX E: EXPANSION OF FUNCTIONS INTO EXPONENTIAL SERIES

402

(1)

APPENDIX F: ELLIPTIC INTEGRALS

403

(2)

References

405

(2)

Index

407

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Electromagnetic Fields: Waves and Numerical Methods

Summary

Table of Contents

Supplemental Materials