Basic Electromagnetism and Materials:Basic Electromagnetism and Materials
Author(s): Andre Moliton
Publisher: Springer; 1 edition
Date : 2006
Pages : 1
Format : PDF
OCR : Yes
Quality :
Language : English
ISBN-10 : 0387302840
ISBN-13 :
Basic Electromagnetism and Materials is the product of many years of teaching basic and applied electromagnetism. This textbook can be used to teach electromagnetism to a wide range of undergraduate science majors in physics, electrical engineering, or materials science. However, by making lesser demands on mathematical knowledge than competing texts, and by emphasizing electromagnetic properties of materials and their applications, this textbook is particularly appropriate for students of materials science. Many competing texts focus on the study of propagation waves either in the microwave or optical domain, whereas Basic Electromagnetism and Materials covers the entire electromagnetic domain and the physical response of materials to these waves.
Review
From the Foreword: Andre Moliton has written a very clear account of electromagnetic radiation generation, and its propagation in free space and various dielectric and conducting media of limited and also infinite dimensions . . . I recommend this book for those interested in the field of electromagnetic radiation and its interaction with matter. The presentation of mathematical derivations combined with comments, figures, descriptions, problems, and solutions results in a refreshing approach to a difficult subject. Both students and researchers will find this book useful and enlightening.
- Arthur J. Epstein, Distinguished University Professor, The Ohio State University
From the reviews:
"Basic Electromagnetism and Materials transcends basic relationships between magnetism and electric current. the material is presented in an approachable manner through the use of detailed summaries of important formulas and the inclusion of comments throughout. Moliton employs full use of constructive exercises and problems in order to reinforce for the student the reliability of results achieved. Four-page index. Summing Up Recommended. Upper-division undergraduates through professionals; Basic also recommended for lower-division undergraduates." (R. C. Jackman, Choice, Vol. 45 (1), 2007)
Contents
Chapter 1. Introduction to the fundamental equations of electrostatics
and magnetostatics in vacuums and conductors……….. 1
1.1. Vectorial analysis……………………………………………………. 1
1.1.1. Operators………………………………………………………. 1
1.1.2. Important formulae……………………………………………. 4
1.1.3. Vectorial integrations…………………………………………. 4
1.1.4. Terminology……………………………………………………. 7
1.2. Electrostatics and vacuums………………………………………… 8
1.2.1. Coulomb's law………………………………………………….. 8
1.2.2. The electric field: local properties and its integral……………. 9
1.2.3. Gauss's theorem………………………………………………… 10
1.2.4. The Laplace and Poisson equations…………………………… 14
1.3. The current density vector: conducting media and electric
currents……………………………………………………………… 16
1.3.1. The current density vector …………………………………….. 16
1.3.2. Local charge conservation equation…………………………... 17
1.3.3. Stationary regimes …………………………………………….. 17
1.3.4. Ohm's law and its limits………………………………………… 20
1.3.5. Relaxation of a conductor……………………………………… 23
1.3.6. Comment: definition of surface current (current sheet)……… 24
1.4. Magnetostatics……………………………………………………….. 24
1.4.1. Magnetic field formed by a current…………………………….. 25
1.4.2. Vector potential ………………………………………………… 26
x Basic electromagnetism and materials
1.4.3. Local properties and the integral of B
􀁇
……………………….… 26
1.4.4. Poisson's equation for the vector potential ……………………. 26
1.4.5. Properties of the vector potential A
􀁇
………………………….… 27
1.4.6. The Maxwell-Ampere relation………………………………….. 28
1.5 Problems…………….……………………………………………….. 31
1.5.1. Calculations……………………………………………………… 31
1.5.2. Field and potential generated inside and outside
of a charged sphere……………….………………………………. 33
Chapter 2. Electrostatics of dielectric materials……………………. 39
2.1. Introduction: dielectrics and their polarization………………..…… 39
2.1.1. Definition of a dielectric and the nature of the charges………… 39
2.1.2. Characteristics of dipoles…………………………………………. 40
2.1.3. Dielectric in a condenser………………………………………… 42
2.1.4. The polarization vector ……………………………………….… 43
2.2. Polarization equivalent charges…………………………………….… 44
2.2.1. Calculation for charges equivalent to the polarization…………. 44
2.2.2. Physical characteristics of polarization and polarization
charge distribution……………………………………………… 46
2.2.3. Important comment: under dynamic regimes the polarization
charges are the origin of polarization currents………………… 50
2.3. Vectors ( ) and an electric displacement ( E
􀁇
D 􀁇 )
:
characteristics at interfaces…………………………………………. 51
2.3.1. Vectors for an electric field (E
􀁇
) and an electric
displacement (D
􀁇
): electric potentials…………………………. 51
2.3.2. Gauss's theorem…………………………..……………………... 52
2.3.3. Conditions under which E
􀁇
and D
􀁇
move between two
dielectrics ………………………………………………………. 53
2.3.4. Refraction of field or induction lines…………………….…….. 56
2.4. Relations between displacement and polarization vectors……… … 56
2.4.1. Coulomb's theorem…………………………..…………………... 56
2.4.2. Representation of the dielectric-armature system…………….… 57
2.4.3. Linear, homogeneous and isotropic dielectrics………………….. 58
2.4.4. Comments………………………………………………………… 59
2.4.5. Linear, inhomogeneous and non-isotropic dielectrics………….. 60
Contents xi
2.5 Problems: Lorentz field………………………………………………. 61
2.5.1. Dielectric sphere ………………………………………………… 61
2.5.2. Empty spherical cavity………………………………………….. 62
2.6. The mechanism of dielectric polarization: response to a static
field…………………………………………………………………… 63
2.6.1. Induced polarization and orientation…………………………… 63
2.6.2. Study of the polarization induced in a molecule………………… 66
2.6.3. Study of polarization by orientation……………………………. 67
2.7. Problems……………………………………………………………… 72
2.7.1. Electric field in a small cubic cavity found within a dielectric….. 72
2.7.2. Polarization of a dielectric strip………………………………... 75
2.7.3. Dielectric planes and charge distribution (electric images)…… 77
2.7.4. Atomic polarizability using J.J. Thomson's model……………. 81
2.7.5. The field in a molecular sized cavity……………………………. 82
Chapter 3: Magnetic properties of materials………………………. 89
3.1. Magnetic moment……………………………………….…………… 89
3.1.1. Preliminary remarks on how a magnetic field cannot be
derived from a uniform scalar potential………………………. 89
3.1.2. The vector potential and magnetic field at a long
distance from a closed circuit…………………………………… 89
3.1.3. The analogy of the magnetic moment to the electric moment..... 93
3.1.4. Characteristics of magnetic moments
S
M 􀀠i􀂳􀂳dS
􀁇 􀁊􀁊􀁇
…………… 94
3.1.5. Magnetic moments in materials………………………………… 97
3.1.6. Precession and magnetic moments……………………………. 98
3.2. Magnetic fields in materials………………………………………… 100
3.2.1. Magnetization intensity………………………………………... 100
3.2.2. Potential vector due to a piece of magnetic material…………. 101
3.2.3. The Amperian currents…………………………………………. 103
3.2.4. Definition of vectorsB 􀁇
and H
􀁇
in materials…………………… 106
3.2.5. Conditions imposed on moving between two magnetic media…. 107
3.2.6. Linear, homogeneous and isotropic (l.h.i) magnetic media….... 109
3.2.7. Comment on the analogy between dielectric and magnetic
media. ……………………………………………………………109
xii Basic electromagnetism and materials
3.3. Problems……………………………………………………………… 111
3.3.1. Magnetic moment associated with a surface charged sphere
turning around its own axis…………………………………………… 111
3.3.2. Magnetic field in a cavity deposited in a magnetic medium…… 112
3.3.3. A cylinder carrying surface currents…………………………... 114
3.3.4 Virtual current…………..………………………………………. 116
Chapter 4: Dielectric and magnetic materials………………………. 119
4.1. Dielectrics……………………………………………………………. 119
4.1.1. Definitions……………………………………………………… 119
4.1.2. Origins and types of breakdowns…………...…………………. 120
4.1.3 Insulators……………………………………………………….. 121
4.1.4 Electrets ………………………………………………………… 123
4.1.5. Ferroelectrics…………………………………………………... 126
4.2. Magnetic materials………………………………………………….. 129
4.2.1. Introduction…………………………………………………….. 129
4.2.2. Diamagnetism and Langevin's theory………………………… 131
4.2.3. Paramagnetism………………………………………………… 132
4.2.4. Ferromagnetism………………………………………………… 137
4.2.5. Antiferromagnetism and ferrimagnetism……………………... 150
4.6. Problem………………………………………………………………. 151
Dielectrics, electrets, magnets, and the gap in spherical armatures… 151
Chapter 5. Time-Varying Electromagnetic Fields and Maxwell’s
equations…………………………………………………. 157
5.1. Variable slow rates and the rate approximation of quasi-static
states (RAQSS)………………………………………………………… 157
5.1.1. Definition……………………..………………………………… 157
5.1.2. Propagation…………………………………………………….. 157
5.1.3. Basics of electromagnetic induction…………………………… 158
5.1.4. Electric circuit subject to a slowly varying rate………………… 158
5.1.5. The Maxwell-Faraday relation………………………………….. 159
Contents xiii
5.2. Systems under frequencies ( div j 􀁺 0
􀁇
) and the Maxwell – Ampere
relation……………………………………………………………….. 160
5.2.1. The shortfall of rot H 􀀠 j􀁁
􀁊􀁊􀁇 􀁇 􀁇
(first form of Ampere's theorem
for static regimes)……………………………………………… 160
5.2.2. The Maxwell-Ampere relation……………………………….. 161
5.2.3. Physical interpretation of the displacement currents…..…… 162
5.2.4. Conclusion……………………………………………………... 165
5.3. Maxwell's equations………………………………………………… 167
5.3.1. Forms of div E and di
􀁇
v B
􀁇
under varying regimes…………... 167
5.3.2. Summary of Maxwell's equations…………………………….. 167
5.3.3. The Maxwell equations and conditions at the interface of two
media………………………………………………………….. 168
5.4. Problem ……………...………………………………………………. 170
Values for conduction and displacement currents in various media… 170
Chapter 6. General properties of electromagnetic waves and their
propagation through vacuums………………………… 173
6.1. Introduction: equations for wave propagation in vacuums……… 173
6.1.1. Maxwell's equations for vacuums: 􀁕􀁁 = 0 and j􀁁 = 0……... 173
6.1.2. Equations of wave propagation………………………………… 173
6.1.3. Solutions for wave propagation equations…………………….. 174
6.2. Different wave types………………………………………………… 176
6.2.1. Transverse and longitudinal waves……………………………. 176
6.2.2. Planar waves…………………………………………………… 176
6.2.3. Spherical waves………………..………………………………… 177
6.2.4. Progressive waves ……………………………………………… 178
6.2.5. Stationary waves………………………………………………… 179
6.3. General properties of progressive planar electromagnetic
waves (PPEMW) in vacuums with 􀁕 􀁁 = 0 and j 􀁁 = 0…………….. 180
6.3.1. E
􀁇
and perpendicular to the propagation: TEM waves……… 181 B
􀁇
6.3.2. The relation between E
􀁇
and B
􀁇
………………………………… 181
6.3.3. Breakdown of a planar progressive electromagnetic wave
(PPEMW) to a superposition of two planar progressive
EM waves polarized rectilinearly………………………………… 183
6.3.4. Representation and spectral breakdown of rectilinearly
polarized PPEMWs………………………………………………. 184
xiv Basic electromagnetism and materials
6.4. Properties of monochromatic planar progressive electromagnetic
waves (MPPEMW)…………………………………………………. 186
6.4.1. The polarization………………………………………………… 186
6.4.2. Mathematical expression for a monochromatic planar wave…. 191
6.4.3. The speed of wave propagation and spatial periodicity………... 194
6.5. Jones's representation……..…………………………………………. 195
6.5.1. Complex expression for a monochromatic planar wave………. 195
6.5.2. Representation by way of Jones's matrix……………………… 196
6.6. Problems……………………………………………………………… 199
6.6.1. Breakdown in real notation of a rectilinear wave into 2
opposing circular waves……………………………………….. 199
6.6.2. The particular case of an anisotropic medium and the
example of a phase retarding strip…………………………..... 200
6.6.3. Jones's matrix based representation of polarization…….…….. 202
Chapter 7. Electromagnetic waves in absorbent and dispersing infinite
materials and the Poynting vector……………………….. 205
7.1. Propagation of electromagnetic waves in an unlimited and
uncharged material for which 􀁕􀁁= 0 and j􀁁 = 0. Expression
for the dispersion of electromagnetic waves………………………… 205
7.1.1. Aide memoir: the Maxwell equation for a material
where 􀁕􀁁 􀀠 0 and j􀁁 􀀠0……………………………………… 205
7.1.2. General equations for propagation……………………………. 205
7.1.3. A monochromatic electromagnetic wave in a linear,
homogeneous and isotropic material………………………. 206
7.1.4. A case specific to monochromatic planar progressive
electromagnetic waves (or MPPEM wave for short)………….. 208
7.2. The different types of media……………………………………….. 210
7.2.1. Non-absorbing media and indices……………………………... 210
7.2.2. Absorbent media, and complex indices………………………… 212
7.3. The energy of an electromagnetic plane wave and the
Poynting vector …………………………………………………….. 215
7.3.1. Definition and physical significance for media of absolute
permittivity (􀁈), magnetic permeability (μ) and subject to a
conduction current (j 􀁁 )…………………………………….. 215
7.3.2. Propagation velocity of energy in a vacuum …………………. 217
Contents xv
7.3.3. Complex notation……………………………………………… 218
7.3.4. The Poynting vector and the average power for a MPPEM
wave in a non-absorbent (k and n are real) and non-magnetic
(μr = 1, so that μ = μ0) medium………………………………… 219
7.3.5. Poynting vector for a MPPEM wave in an absorbent
dielectric such that μ is real………………………………. 219
7.4 Problem……………………………………………………………….. 220
Poynting vector………………………………………………………... 220
Chapter 8. Waves in plasmas and dielectric, metallic, and magnetic
materials ……………………………………………….. 227
8.1. Interactions between electromagnetic wave and materials…………227
8.1.1. Parameters under consideration………………………………….227
8.1.2. The various forces involved in conventionally studied
materials……………………………………………………… 228
8.2. Interactions of EM waves with linear, homogeneous and isotropic
(lhi) dielectric materials: electronic polarization, dispersion and
absorption…………………………………………………………….. 229
8.2.1. The Drude Lorentz model……………………………………… 231
8.2.2. The form of the polarization and the dielectric permittivity….. 232
8.2.3. Study of the curves 􀁆 e’(􀁚) and 􀁆 e’’(􀁚) for 􀁚 􀁼 􀁚 0 …………….. 234
8.2.4. Study of the curves of 􀁆 e’(􀁚) and 􀁆 e’’(􀁚) when 􀁚 􀁺 􀁚0 …….. 238
8.2.5. The (zero) pole of the dielectric function……………………… 240
8.2.6. Behavior of a transverse plane progressive EM wave which
has a pulsation between 􀁚 0 and 􀁚 􀁁 sufficiently far from
􀁚 0
so that 􀁈’’ 􀁼 0……………………………………………… 241
8.2.7. Study of an MPPEM wave both outside the absorption zone
and the range [ 􀁚 0,􀁚 􀁁]………………………………………… 241
8.2.8. Equation for dispersion n = f( 􀁏 0) when 􀁚 << 􀁚 0………………. 243
8.3. Propagation of a MPPEM wave in a plasma (or the dielectric
response of an electronic gas)……………………………………... 245
8.3.1. Plasma oscillations and pulsations……………………………. 245
8.3.2. The dielectric response of an electronic gas………………….. 248
8.4. Propagation of an EM wave in a metallic material (frictional
forces)…………………………………………………………….. 252
xvi Basic electromagnetism and materials
8.5. Uncharged magnetic media…………………………………………. 256
8.5.1. Dispersion equation in conducting magnetic media…………… 256
8.5.2. Impedance characteristics (when k is real)…………………… 257
8.6. Problems……………………………………………………………… 258
8.6.1. The complex forms for polarisation and dielectric
permittivity…………………………………………………….. 258
8.6.2. A study of the electrical properties of a metal ………………… 263
Chapter 9. Electromagnetic field sources, dipolar radiation and
antennae………………………………………………….. 267
9.1. Introduction………………………………………………………… 267
9.2. The Lorentz gauge and retarded potentials ……………………… 268
9.2.1. Lorentz's gauge………………………………………………… 268
9.2.2. Equation for the propagation of potentials, and retarded
potentials ………………………………………………………. 273
9.3. Dipole field at a great distance …………………………….………. 275
9.3.1. Expression for the potential vector A
􀁇
………………………… 275
9.3.2. Expression for the electromagnetic field in the radiation zone .. 277
9.3.3. Power radiated by a dipole……………………………………… 278
9.4. Antennas………..…………………………………………………….. 280
9.4.1. Principle: a short antenna where 􀁁 << 􀁏…………………..…… 280
9.4.2. General remarks on various antennae: half-wave and 'whip'
antennae ………………………………………………………….. 283
9.5.Problem ……………………….……………………………………… 285
Radiation from a half-wave antenna….………………………………. 286
Chapter 10. Interactions between materials and electromagnetic
waves, and diffusion and absorption processes………. 289
10.1. Introduction………………………………………………………… 289
10 .2. Diffusion mechanisms …………………………………………….. 289
10.2.1. Rayleigh diffusion: radiation diffused by charged particles.… 289
10.2.2. Radiation due to Rutherford diffusion………………………... 294
Contents xvii
10.3. Radiation produced by accelerating charges: synchrotron
radiation and bremsstrahlung………………………………………..297
10.3.1. Synchrotron radiation……………………….………………… 297
10.3.2. Bremsstrahlung: electromagnetic stopping radiation………... 297
10. 4. Process of absorption or emission of electromagnetic radiation by
atoms or molecules (to approach as part of a second reading) …... 298
10.4.1. The problem…………………………………………………… 298
10.4.2. Form of the interaction Hamiltonian………………………… 298
10.4.3. Transition rules………………………………………………... 302
10.5. Conclusion: introduction to atomic and molecular spectroscopy... 306
10.5.1. Result concerning the dipole approximation…………………. 306
10.5.2. Different transitions possible in an electromagnetic
spectrum………………………………………………………… 307
10.5.3. Conclusion…………………………………………………….. 309
10.6. Problems……………………………………………………………. 309
10.5.1. Problem 1. Diffusion due to bound electrons………………… 309
10.5.2. Problem 2. Demonstration of the relationship between matrix
elements………………………………………………………… 313
Chapter 11. Reflection and refraction of electromagnetic waves in
absorbent materials of finite dimensions……………… 317
11.1. Introduction………………………………………………………... 317
11.2. Law of reflection and refraction………………………………….. 318
11.2.1. Representation of the system……………………………………318
11.2.2. Conservation of angular frequency …………………………. 319
11.2.3. Form of the wave vectors with respect to the symmetry of the
media…………………………………………………………. 320
11.2.4. Symmetry and linear properties of the media …….…………. 321
11.2.5. Snell-Descartes law ……………..……………………………. 322
11.2.6. Equation for the electric field in medium (1): the law of
reflection……………………………………………………… 323
11.2.7. The Snell-Descartes law for reflection a system where medium
(2) can be absorbent: n2 and k2 are complex ……………….. 325
11.3. Coefficients for reflection and transmission of a monochromatic
plane progressive EM wave at the interface between two nonabsorbent
lhi dielectrics (n1 , n2 real), and the Fresnel equations….331
xviii Basic electromagnetism and materials
11.3.1. Hypothesis and aim of the study……………………………... 331
11.3.2. Fresnel equations for perpendicular polarizations (TE)……. 333
11.3.3. Fresnel's equations for parallel magnetic field polarizations.. 337
11.3.4. Reflection coefficients and energy transmission ……………... 342
11.3.5. Total and frustrated total reflection………………………….. 346
11.4. Reflection and absorption by an absorbing medium …………… 348
11.4.1. Reflection coefficient for a wave at a normal incidence to an
interface between a non-absorbent medium (1) (index of n1)
and an absorbent medium (2) (index of n2 )…………….…… 348
11.4.2. Optical properties of a metal: reflection and absorption at
low and high frequencies by a conductor…………………… 349
11.5. The anti-echo condition: reflection from a magnetic layer; a
study of an anti-radar structure; and a Dallenbach layer………….350
11.5.1. The anti-echo condition: reflection from a non-conducting
magnetic layer……………….................................................. 350
11.5.2. The Dallenbach layer: an anti-radar structure……………… 352
11.6. Problems…………………………………………………………….. 356
11.6.1. Reflection and absorption at low and high frequencies by a
conductor………………………………………………………. 356
11.6.2. Limited penetration of Hertzian waves in sea water……………362
Chapter 12. Total reflection and guided propagation of
electromagnetic waves in materials of finite
dimensions……………………………………………. 367
12.1. Introduction……………………………………………………….. 367
12.2. A coaxial line……………………………………………………….. 369
12.2.1. Form of transverse EM waves in a coaxial cable……………. 369
12.2.2. Form of the potential, the intensity, and the characteristic
impedance of the cable……….………………………………… 371
12.2.3. Electrical power transported by an EM wave………….…….. 373
12.2.4. Conductor with an imperfect core …………………..……….. 374
12.3. Preliminary study of the normal reflection………………….…… 374
12.3.1. Properties of a perfect conductor…………………………….. 374
12.3.2. Equation for the stationary wave following reflection……… 376
12.3.3. Study of the form of the surface charge densities and the
current at the metal……………………………………………. 377
Contents xix
12.4. Study of propagation guided between two plane conductors…… 380
12.4.1. Wave form and equation for propagation …………………... 380
12.4.2. Study of transverse EM waves ………………………………. 381
12.4.3. Study of transverse electric waves (TE waves)………………. 383
12.4.4. Generalization of the study of TE wave propagation………… 388
12.5. Optical guiding: general principles and how fibers work………. 399
12.5.1. Principle………………………………………………………. 399
12.5.2. Guiding conditions…………………………………………… 400
12.5.3. Increasing the signals………………………………………… 401
12.6. Electromagnetic characteristics of a symmetrical monomodal
guide……………………………………………………………… 402
12.6.1. General form of the solutions………………………………... 403
12.6.2. Solutions for zone (2) with an index denoted by n…………… 404
12.6.3. Solutions for the zones (1) and (3)…………………………… 405
12.6.4. Equations for the magnetic field…………………………….. 408
12.6.5. Use of the limiting conditions: determination of constants…. 408
12.6.6. Modal equation………………………………………………. 410
12.6.7. Comments: alternative methodologies ……………………… 415
12.6.8. Field distribution and solution parity……………………….. 417
12.6.9. Guide characteristics…………………………………………. 419
12.7. Problem……………………………………………………………… 423
Monomodal conditions……………………………………………….. 423
Index ………………………………………………………………….. 427
Basic Electromagnetism and Materials
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