Lehner G. Electromagnetic Field Theory for Engineers and Physicists

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654 Index I

identity operator 160

identity tensor 160

image charge 56, 74–80, 95, 97, 138,

200, 205, 227

image charge method

537, 562–563

image currents 314

image field

374

image source 243

implicit methods

549

improper functions 132

inductance coefficients 336

induction

-magnetic

inertial systems 616, 627

infinite elements

556

influence charge 73, 205

influence coefficients 202, 204

inhomogeneous wave

428, 440, 441

inhomogeneous wave equation 444, 573

initial curve 299

initial value problems

357, 360, 361

inner conductor 492

insulator 72

insulators

integral

-total elliptic of the 1st kind 174, 277

-total elliptic of the 2nd kind

277

integral operator 163

integral transform 163, 165, 366, 371

integration by parts

130

Interference of electron beams 599

interference pattern 599

invariance of Maxwell’s equations in

dual transformations

588

invariant 588

inverse formulation

559

ionosphere 583

irreversible process

354

irrotational

19, 100

iteration method

543, 548

Jacobi method 548

Joule

37, 39

Jupiter

583

Kelvin function

-"ber" and "bei" 400

kernel of the integral transform 164

kilogram

Kirchhoff’s theorem 137, 506, 510, 515,

562

-one-dimensional

510

Kirchhoff’s theorem on electric circuits

theory

233

Klein-Gordon equation 570

Kronecker symbol 144

l’Hospital’s rule 364

Lagrange multiplier 519, 521

Lagrange parameter, see Lagrange multi-

plier

Laplace operator

41, 136, 257, 258, 545

Laplace transform 357

Laplace’s equation

41, 518

Laplacian, see Laplace operator

Laplacie Operator 117, 122

Laurent series

363

law of refraction 103, 241, 242, 432

-for g and E lines 238

least squares

529, 530, 532, 536

Legendre polynomials 190, 611

light conductor 486

light guide

486

light quanta 569, 575, 582

lightly populated matrices 543

line dipole

69, 225

linear polarization 416

linearity 32

linearly polarized

411

local grid refinement 548

local interaction 594

location coordinates, canonical

594

logarithmic potential

longitudinal waves 407

Lorentz contraction

Lorentz force 29, 256, 344, 345

Lorentz gauge

257, 443

Lorentz transformation

618

Lorentz-contraction

623

LR decomposition

548

Index M 655

magnet 85

magnetic charge 29, 35, 585–593

magnetic charges 23

magnetic circuit

303

magnetic conductivity 304

magnetic dipole

-oscillating

463

magnetic dipole layer 282

magnetic dipole moment

279, 290, 293

magnetic dipoles 286

magnetic field 23

magnetic field strength

magnetic field strength definition 295

magnetic flux 30, 262, 325, 341, 343

magnetic flux density

magnetic needle 23

magnetic resistance 304

magnetic surface

326

magnetization 286

magnetization current 315–320

magnetization current density

288

magnetostatics 34, 256

mapping 213

-conformal

210, 215

-conformal mapping 215, 216, 219,

220, 227, 231, 242, 247, 251, 265,

269, 322

material equation

materials

-hard

301

-soft 301

Maxwell’s equations 1

Maxwell’s equations - supplement

mean value theorems of potential theory

515, 516, 542

medium

-infinitely conductive

320

-magnetizable

295

metallic cylinder

metallic sphere

meter 35

method

-of complex analysis

117

-of function theory

209

-of image charges

138

-of separation of variables

117

-of virtual displacement

115

method of images

metric tensor 121

Michelson experiment 617

Minkowski space

620, 629

mirror charge, see also image charge

m-mesons 624

moment, magnetic

286

momentum

-operator of

569

Momentum Method 536

momentum method 528, 532

monopole

198

-magnetic 585, 587, 593

Monte-Carlo method 537, 539, 563–568

multi-conductor systems

200

multiply connected regions 263

multipole expansion 198

Nabla 12, 17

natural boundary conditions 518, 519

natural phenomenon 35

net forces

Neumann boundary value problem 470

Neumann function 166

Neumann’s boundary value problem

128

Newton 37

nine-point formula 544, 547

nodal points

550–556, 561

nodal points of a standing wave 417

nodes of a standing wave 417

noise

355

normal component of B 306

normal component of D 65, 87, 153

normal components of D

242

octopole moment 198

Ohm

39, 235

Ohm’s law

32, 110, 232

orthogonal grid

208

orthogonal trajectory 208

orthogonal transformation

618

orthogonality relation

144, 146, 148,

153, 156, 157–159, 161, 173, 182, 191

overdetermined collocation

529–532,

536, 562

656 Index P

paramagnetic 294

paramagnetism 294

parameter representation 118

partial differential equations

-elliptic

355

-hyperbolic 355

-parabolic

355

p-domain 362, 370, 382, 391, 399, 503

penetration depth

378, 402

penetration depths 401

period 412

permanent magnet

297

permeability

-absolute 296

-relative

296

permeability of vacuum 29

permittivity 4, 86

perpetuum mobile

phase constant 427

phase velocity 359, 378, 412–419, 430,

476, 488, 580

photon

photon rest mass 572

plane case

plane electrostatic problems 206

plane of incidence 92, 432, 433

plane waves

407–439

plate, planar, in magnetic field 307

plate, plane, in electric field 85

p-Mesons

571

point charge 8, 44, 93, 134, 154, 174, 175

Poisson’s equation 41, 49, 135, 149, 151,

518, 520–529

-magnetic

297

polar plot 461

polarization

60, 84, 97

-circular 416

-elliptical

415

-linear

415

-magnetic

290

-parallel 433

-permanent

-perpendicular

433

polarization angle.

437

polarization current

106

polarization current density

107

polarization potentials.

451

polarized - permanently

pole of order m 363

pole of order m, 364

potential

19–21, 41–44, 136

-discontinuity 71

-scalar magnetic 263

potential coefficients

202

potential difference

204

potential equation

356

potential function 19, 40

potential theory 128

Poynting vector

423, 460, 461, 464, 573

Poynting vector. 108

Poynting’s theorem 573

principle for conservation of electric

charges

27, 107, 232, 262, 586

Principle of charge conservation 27, 33

Proca equations

572, 582

Proca-equations 572

process

-irreversible

355

-stochastic 358

projection operator 160

propagation vector

414

pseudo-Euclidean four-dimensional

space-time 620

quadrupole 198

quantization of the angular momentum

586

Quantum electrodynamics

Quantum Mechanics 569

quark 27

quasi stationary approximation

343

radiation power 461–463

radiation resistance

462, 465

rank reduction

630

Rayleigh-Ritz method

519

reciprocity theorem 204

reference function

517

reference point

reflectance

437

refraction

-at a boundary

-due to free surface charges

Index S 657

-for magnetic field lines 306

-of electric force lines 90–92

-of waves 439

relative dielectric constant,

relativistic Doppler effect 626

relativistic particle 581

relativistically invariant

639

Relativity, Theory of

relaxation method

548

remanence 299

remanent field 299

residual

528

resistance 39, 110, 234, 251

-magnetic 304

resonant cavity

481

resonant frequency 483

rest mass of photons 10, 569–584

retarded solution

446

Riemann surface 221

Ritz method 519

Rotation, see curl

rotation, see curl

saturation 299

scale factor

120

Schrödinger’s equation 569, 594–599

-relativistic 570

Schumann-resonance

583

Schwarz-Christoffel mapping 231

Second 35