Electromagnetic field theory

Electromagnetic field theory

Автор(ы): Thide B.

06.10.2007
Год изд.: 2002
Описание: This book intended primarily as a textbook for physics students at the advanced undergraduate or beginning graduate level, the book may be useful for research workers too. It provides a thorough treatment of the theory of electrodynamics, mainly from a classical field theoretical point of view, and includes such things as electrostatics and magnetostatics and their unification into electrodynamics, the electromagnetic potentials, gauge transformations, covariant formulation of classical electrodynamics, force, momentum and energy of the electromagnetic field, radiation and scattering phenomena, electromagnetic waves and their propagation in vacuum and in media, and covariant Lagrangian/Hamiltonian field theoretical methods for electromagnetic fields, particles and interactions. The aim for the author has been to write a book that can serve both as an advanced text in Classical Electrodynamics and as a preparation for studies in Quantum Electrodynamics and related subjects.
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1 Classical Electrodynamics [1]
1.1 Electrostatics [2]
1.1.1 Coulomb’s law [2]
1.1.2 The electrostatic field [3]
1.2 Magnetostatics [6]
1.2.1 Ampere’s law [6]
1.2.2 The magnetostatic field [7]
1.3 Electrodynamics [9]
1.3.1 Equation of continuity for electric charge [10]
1.3.2 Maxwell’s displacement current [10]
1.3.3 Electromotive force [11]
1.3.4 Faraday’s law of induction [12]
1.3.5 Maxwell’s microscopic equations [15]
1.3.6 Maxwell’s macroscopic equations [16]
1.4 Electromagnetic Duality [16]
Example 1.1 Faraday’s law as a consequence of conservation of magnetic charge [18]
Example 1.2 Duality of the electromagnetodynamic equations [19]
Example 1.3 Dirac’s symmetrised Maxwell equations for a fixed mixing angle [20]
Example 1.4 The complex field six-vector [21]
Example 1.5 Duality expressed in the complex field six-vector [22]
Bibliography [23]
2 Electromagnetic Waves [25]
2.1 The Wave Equations [26]
2.1.1 The wave equation for E [26]
2.1.2 The wave equation for В [26]
2.1.3 The time-independent wave equation for E [27]
Example 2.1 Wave equations in electromagnetodynamics [28]
2.2 Plane Waves [30]
2.2.1 Telegrapher’s equation [31]
2.2.2 Waves in conductive media [32]
2.3 Observables and Averages [34]
Bibliography [35]
3 Electromagnetic Potentials [37]
3.1 The Electrostatic Scalar Potential [37]
3.2 The Magnetostatic Vector Potential [38]
3.3 The Electrodynamic Potentials [38]
3.3.1 Electrodynamic gauges [40]
Lorentz equations for the electrodynamic potentials [40]
Gauge transformations [41]
3.3.2 Solution of the Lorentz equations for the electromagnetic potentials [42]
The retarded potentials [46]
Example 3.1 Electromagnetodynamic potentials [46]
Bibliography [47]
4 Relativistic Electrodynamics [49]
4.1 The Special Theory of Relativity [49]
4.1.1 The Lorentz transformation [50]
4.1.2 Lorentz space [51]
Radius four-vector in contravariant and covariant form [52]
Scalar product and norm [52]
Metric tensor [53]
Invariant line element and proper time [54]
Four-vector fields [56]
The Lorentz transformation matrix [56]
The Lorentz group [56]
4.1.3 Minkowski space [57]
4.2 Covariant Classical Mechanics [59]
4.3 Covariant Classical Electrodynamics [61]
4.3.1 The four-potential [61]
4.3.2 The Lienard-Wiechert potentials [62]
4.3.3 The electromagnetic field tensor [64]
Bibliography [67]
5 Electromagnetic Fields and Particles [69]
5.1 Charged Particles in an Electromagnetic Field [69]
5.1.1 Covariant equations of motion [69]
Lagrange formalism [70]
Hamiltonian formalism [72]
5.2 Covariant Field Theory [76]
5.2.1 Lagrange-Hamilton formalism for fields and interactions [76]
The electromagnetic field [80]
Example 5.1 Field energy difference expressed in the field tensor [81]
Other fields [84]
Bibliography [85]
6 Electromagnetic Fields and Matter [87]
6.1 Electric Polarisation and Displacement [87]
6.1.1 Electric multipole moments [87]
6.2 Magnetisation and the Magnetising Field [90]
6.3 Energy and Momentum [92]
6.3.1 The energy theorem in Maxwell’s theory [92]
6.3.2 The momentum theorem in Maxwell’s theory [93]
Bibliography [95]
7 Electromagnetic Fields from Arbitrary Source Distributions [97]
7.1 The Magnetic Field [99]
7.2 The Electric Field [101]
7.3 The Radiation Fields [103]
7.4 Radiated Energy [106]
7.4.1 Monochromatic signals [106]
7.4.2 Finite bandwidth signals [107]
Bibliography [108]
8 Electromagnetic Radiation and Radiating Systems [109]
8.1 Radiation from Extended Sources [109]
8.1.1 Radiation from a one-dimensional current distribution [110]
8.1.2 Radiation from a two-dimensional current distribution [113]
8.2 Multipole Radiation [116]
8.2.1 The Hertz potential [116]
8.2.2 Electric dipole radiation [120]
8.2.3 Magnetic dipole radiation [122]
8.2.4 Electric quadrupole radiation [123]
8.3 Radiation from a Localised Charge in Arbitrary Motion [124]
8.3.1 The Lienard-Wiechert potentials [125]
8.3.2 Radiation from an accelerated point charge [127]
The differential operator method [129]
Example 8.1 The fields from a uniformly moving charge [134]
Example 8.2 The convection potential and the convection force [136]
Radiation for small velocities [139]
8.3.3 Bremsstrahlung [140]
Example 8.3 Bremsstrahlung for low speeds and short acceleration times [143]
8.3.4 Cyclotron and synchrotron radiation [145]
Cyclotron radiation [147]
Synchrotron radiation [148]
Radiation in the general case [150]
Virtual photons [151]
8.3.5 Radiation from charges moving in matter [153]
Vavilov-Cerenkov radiation [155]
Bibliography [160]
F Formulae [161]]
F.1 The Electromagnetic Field [161]
F.1.1 Maxwell’s equations [161]
Constitutive relations [161]
F.1.2 Fields and potentials [161]
Vector and scalar potentials [161]
Lorentz’gauge condition in vacuum [162]
F.1.3 Force and energy [162]
Poynting’s vector [162]
Maxwell’s stress tensor [162]
F.2 Electromagnetic Radiation [162]
F.2.1 Relationship between the field vectors in a plane wave [162]
F.2.2 The far fields from an extended source distribution [162]
F.2.3 The far fields from an electric dipole [162]
F.2.4 The far fields from a magnetic dipole [163]
F.2.5 The far fields from an electric quadrupole [163]
F.2.6 The fields from a point charge in arbitrary motion [163]
F.3 Special Relativity [163]
F.3.1 Metric tensor [163]
F.3.2 Covariant and contravariant four-vectors [164]
F.3.3 Lorentz transformation of a four-vector [164]
F.3.4 Invariant line element [164]
F.3.5 Four-velocity [164]
F.3.6 Four-momentum [164]
F.3.7 Four-current density [164]
F.3.8 Four-potential [164]
F.3.9 Field tensor [165]
F.4 Vector Relations [165]
F.4.1 Spherical polar coordinates [165]
Base vectors [165]
Directed line element [165]
Solid angle element [166]
Directed area element [166]
Volume element [166]
F.4.2 Vector formulae [166]
General vector algebraic identities [166]
General vector analytic identities [166]
Special identities [167]
Integral relations [167]
Bibliography [168]
Appendices [169]
M Mathematical Methods [169]
M.1 Scalars, Vectors and Tensors [169]
M.1.1 Vectors [169]
Radius vector [169]
M.1.2 Fields [171]
Scalar fields [171]
Vector fields [171]
Tensor fields [172]
Example M.I Tensors in 3D space [173]
Example M.2 Contravariant and covariant vectors in flat Lorentz space [176]
M.1.3 Vector algebra [178]
Scalar product [178]
Example M.3 Inner products in complex vector space [178]
Example M.4 Scalar product, norm and metric in Lorentz space [179]
Example M.5 Metric in general relativity [180]
Dyadic product [181]
Vector product [181]
M.1.4 Vector analysis [182]
The del operator [182]
Example M.6 The four-del operator in Lorentz space [183]
The gradient [183]
Example M.7 Gradients of scalar functions of relative distances in 3D [183]
The divergence [184]
Example M.8 Divergence in 3D [184]
TheLaplacian [185]
Example M.9 The Laplacian and the Dirac delta [185]
The curl [185]
Example M. 10 The curl of a gradient [185]
Example M. 11 The divergence of a curl [186]
M.2 Analytical Mechanics [187]
M.2.1 Lagrange’s equations [187]
M.2.2 Hamilton’s equations [188]
Bibliography [188]

1.1 Coulomb interaction between two electric charges [3]
1.2 Coulomb interaction for a distribution of electric charges [5]
1.3 Ampere interaction [7]
1.4 Moving loop in a varying В field [13]
4.1 Relative motion of two inertial systems [50]
4.2 Rotation in a 2D Euclidean space [57]
4.3 Minkowski diagram [58]
5.1 Linear one-dimensional mass chain [77]
7.1 Radiation in the far zone [105]
8.1 Linear antenna [110]
8.2 Electric dipole geometry [111]
8.3 Loop antenna [113]
8.4 Multipole radiation geometry [118]
8.5 Electric dipole geometry [121]
8.6 Radiation from a moving charge in vacuum [125]
8.7 An accelerated charge in vacuum [128]
8.8 Angular distribution of radiation during bremsstrahlung [141]
8.9 Location of radiation during bremsstrahlung [142]
8.10 Radiation from a charge in circular motion [146]
8.11 Synchrotron radiation lobe width [148]
8.12 The perpendicular field of a moving charge [151]
8.13 Vavilov-Cerenkov cone [157]
M.I Tetrahedron-like volume element of matter [174]

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