Introduction to Classical Electrodynamics, Volume 2 - Boucif Abdesselam

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Auteur(s) : Boucif Abdesselam

Editeur : Wiley

Langue : Anglais

Parution : 01/09/2025

Format : Moyen, de 350g à 1kg

Nombre de pages : 448.0

ISBN : 9781836690016

Résumé :

Since Maxwell's time, electromagnetic theory has made spectacular progress, particularly in the field of waves. Introduction to Classical Electrodynamics 2 presents the fundamental concepts of electromagnetic field theory.

This book first addresses static potentials with sources and provides a detailed presentation of the method of images and Green's functions. It also analyzes electromagnetic induction phenomena and Maxwell's equations. It examines electromagnetic waves in a vacuum and their properties, as well as the concept of electromagnetic energy. Finally, it covers polarized and magnetized media, along with electromagnetic fields and their propagation in material media.

This book is intended for physics and mathematics students, as well as engineering students interested in the challenges of electromagnetic theory. The discussion is supplemented with numerous applications derived from the theoretical concepts presented.

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Biographie:

Boucif Abdesselam is a professor in the Physics Department of the Faculty of Science and Technology at the Universit? Ain Temouchent Belhadj Bouchai, Algeria. He is also a member of the Theoretical Physics Laboratory at the University of Oran 1, Algeria.

Sommaire:

Preface ix

Chapter 1 Static Potentials with Sources 1

1.1. Poisson equation 1

1.2. The image charge method 6

1.2.1. General properties 6

1.2.2. Point charge in proximity to a conducting plane 7

1.2.3. Point charge in proximity to a conducting sphere 15

1.2.4. Dipole in proximity to a conducting sphere 23

1.2.5. Infinite line charge in proximity to a plane 26

1.2.6. Infinite line charge in proximity to a conducting cylinder 27

1.3. Green's function 34

1.3.1. Position of the problem 34

1.3.2. Poisson equation solutions 34

1.3.3. Green's theorem 36

1.3.4. Inverse Laplacian and Green's function 36

1.3.5. Derivation of the Green's function by the Fourier transform 39

1.4. Integral form of the Poisson equation 40

1.5. Expansion of Green's function on spherical harmonics 43

1.6. Green-Dirichlet function from its differential equation 49

1.7. Eigenfunctions method 55

Chapter 2 Electromagnetic Induction Phenomena 59

2.1. Experimental observations 59

2.2. EMF for static fields (Lorentz case) 66

2.3. Variable magnetic field (Neumann case) 71

VI Introduction to Classical Electrodynamics 2

2.3.1. Motion relative to the fixed reference Oxyz 71

2.3.2. Motion Relative to the Moving Frame O ? X ? Y ? Z ? Attached to the circuit 73

2.3.3. Maxwell-Faraday equation 75

2.4. General case of a deformable circuit 76

2.4.1. Electromotive field and induced EMF 76

2.4.2. Faraday's law 76

2.5. Maxwell-Amp?re equation and displacement current 81

2.6. Lorentz force and canonical momentum 85

2.7. Maxwell equations 88

2.8. Gauge transformations 88

Chapter 3 Electromagnetic Waves in a Vacuum 95

3.1. Wave equations in a vacuum 95

3.2. One-dimensional solutions 98

3.3. Structure of a plane electromagnetic wave 102

3.4. Progressive plane monochromatic waves (PPMW) 104

3.4.1. Sinusoidal solutions of the d'Alembert propagation equation 104

3.4.2. Complex representation of PPMWs 111

3.4.3. Polarization of a PPMW 113

3.5. Interference of light waves 124

3.6. Transverse electric (TE) and transverse magnetic (TM) spherical waves 132

Chapter 4 Electromagnetic Energies 137

4.1. Energy stored in a charged distribution 137

4.1.1. Electrostatic potential energy of a distribution of point charges 138

4.1.2. Electrostatic energy of a continuous charge distribution 143

4.1.3. Energy stored in the electric field 147

4.1.4. Electrostatic interaction energy between two fields 150

4.2. Electrostatic actions on a conductor in equilibrium 153

4.2.1. Concepts of rigid body mechanics 153

4.2.2. Electrostatic actions from electrostatic energy 155

4.3. Magnetic actions 159

4.3.1. Laplace force - Moment of Laplace force 159

4.3.2. Magnetic moment of a closed circuit in a constant magnetic field 160

4.3.3. Expressions of actions from magnetic energy 161

4.4. Action of a magnetic field on a conductor: magnetoresistance 163

4.5. Magnetic inductances 166

4.5.1. Neumann formula 166

4.5.2. Inductance matrix 170

4.5.3. Mutual inductance coupling 175

4.6. Electromagnetic energy 184

4.6.1. Magnetic energy of a set of n thin-wire circuits 184

4.6.2. Magnetic energy of a volume current distribution 184

4.6.3. Poynting's theorem 190

4.7. Maxwell tensor 194

4.7.1. Maxwell stress tensor for the electric field 194

4.7.2. Maxwell stress tensor for the magnetic field 197

4.7.3. Maxwell stress ten...