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Format: XVIII, 374 p. 128 illus., 6 illus. in color. , online resource.

Edition: 2nd ed. 2022.

ISBN: 9783031050992

Series Statement: Undergraduate Lecture Notes in Physics,

Content: This book presents an overview of Classical Electrodynamics. Its second edition includes new chapters that pick up where the material from the first edition left off. The image method introduced in the first edition is expanded to series of images, using simple examples like a point charge or a charged wire between two grounded plates, as well as more relevant examples such as two charged conducting spheres and the force between them. The topic of complex functions is broadened with the introduction of conformal mapping. One new chapter introduces the method of separation of variables, including in Cartesian coordinates (box with sides at fixed voltages), in spherical coordinates (dielectric and conducting sphere, potential of a charged ring), in cylindrical coordinates (conducting wedge, cylinder in uniform field). It also presents the potentials and the fields for a point charge in motion, radiation by a point charge and by a dipole, radiation reaction. Two other chapters present updated lessons on the mass of the photon and search for monopoles. Examples and/or solvable problems are provided throughout.

Note: 1 Classical Electrodynamics: a short review -- 2 Multipole expansion of the potential -- 3 The method of image charges -- 4 Image charges in dielectrics -- 5 Series of image charges -- 6 Functions of complex variables and Electrostatics -- 7 Conformal mapping in Electrostatics -- 8 Separation of Variables in Laplace Equation -- 9 Relativistic transformation of E and B fields -- 10 Relativistic covariance of Electrodynamics -- 11 The resonant cavity -- 12 Energy and momentum of the electromagnetic field -- 13 The Feynman paradox -- 14 Fields, potentials and radiation -- 15 Test of of the Coulomb's law and limits on the mass of the photon -- 16 Magnetic monopoles -- A Orthogonal curvilinear coordinates.

In: Springer Nature eBook

Additional Edition: Printed edition: ISBN 9783031050985

Additional Edition: Printed edition: ISBN 9783031051005

Language: English

Subjects: Physics

DOI: 10.1007/978-3-031-05099-2

URL: https://doi.org/10.1007/978-3-031-05099-2

URL: Volltext  (URL des Erstveröffentlichers)

UID:

Format: 1 Online-Ressource (xviii, 374 Seiten) , Illustrationen, Diagramme

Edition: Second edition

ISBN: 9783031050992

Series Statement: Undergraduate lecture notes in physics

Content: 1 Classical Electrodynamics: a short review -- 2 Multipole expansion of the potential -- 3 The method of image charges -- 4 Image charges in dielectrics -- 5 Series of image charges -- 6 Functions of complex variables and Electrostatics -- 7 Conformal mapping in Electrostatics -- 8 Separation of Variables in Laplace Equation -- 9 Relativistic transformation of E and B fields -- 10 Relativistic covariance of Electrodynamics -- 11 The resonant cavity -- 12 Energy and momentum of the electromagnetic field -- 13 The Feynman paradox -- 14 Fields, potentials and radiation -- 15 Test of of the Coulomb’s law and limits on the mass of the photon -- 16 Magnetic monopoles -- A Orthogonal curvilinear coordinates.

Content: This book presents an overview of Classical Electrodynamics. Its second edition includes new chapters that pick up where the material from the first edition left off. The image method introduced in the first edition is expanded to series of images, using simple examples like a point charge or a charged wire between two grounded plates, as well as more relevant examples such as two charged conducting spheres and the force between them. The topic of complex functions is broadened with the introduction of conformal mapping. One new chapter introduces the method of separation of variables, including in Cartesian coordinates (box with sides at fixed voltages), in spherical coordinates (dielectric and conducting sphere, potential of a charged ring), in cylindrical coordinates (conducting wedge, cylinder in uniform field). It also presents the potentials and the fields for a point charge in motion, radiation by a point charge and by a dipole, radiation reaction. Two other chapters present updated lessons on the mass of the photon and search for monopoles. Examples and/or solvable problems are provided throughout.

Additional Edition: ISBN 9783031050985

Additional Edition: ISBN 9783031051005

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9783031050985

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9783031051005

Language: English

DOI: 10.1007/978-3-031-05099-2

URL: lizenzpflichtig

URL: lizenzpflichtig

UID:

Format: 1 online resource (379 pages)

Edition: Second edition.

ISBN: 9783031050992

Series Statement: Undergraduate lecture notes in physics

Note: Intro -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- 1 Classical Electrodynamics: A Short Review -- 1.1 Coulomb's Law and the First Maxwell Equation -- 1.2 Charge Conservation and Continuity Equation -- 1.3 Absence of Magnetic Charges in Nature and the Second Maxwell Equation -- 1.4 Laplace's Laws, Biot and Savart Law and the Steady Fourth Maxwell Equation -- 1.5 Faraday's Law and the Third Maxwell Equation -- 1.6 Displacement Current and the Fourth Maxwell Equation -- 1.7 Maxwell Equations in Vacuum -- 1.8 Maxwell Equations in Matter -- 1.9 Electrodynamic Potentials and Gauge Transformations -- 1.10 Electromagnetic Waves -- References -- 2 Multipole Expansion of the Electrostatic Potential -- 2.1 The Potential of the Electric Dipole -- 2.2 Interaction of the Dipole with an Electric Field -- 2.3 Multipole Expansion for the Potential of a Distribution of Point Charges -- 2.4 Properties of the Electric Dipole Moment -- 2.5 The Quadrupole Tensor -- 2.6 A Bidimensional Quadrupole -- Problems -- Solutions -- References -- 3 The Method of Image Charges -- 3.1 The Method of Image Charges -- 3.2 Point Charge and Conductive Plane -- 3.3 Point Charge and Conducting Sphere -- 3.3.1 Force on a Point Charge Near a Charged Conducting Sphere -- 3.4 Conducting Sphere in a Uniform Electric Field -- 3.5 A Charged Wire Near a Cylindrical Conductor -- Problems -- Solutions -- References -- 4 Image Charges in Dielectrics -- 4.1 Electrostatics in Dielectric Media -- 4.2 Point Charge Near the Plane Separating Two Dielectric Media -- 4.3 Dielectric Sphere in an External Uniform Electric Field -- Problems -- Solutions -- References -- 5 Series of Image Charges -- 5.1 Point Charge Between Two Grounded Plates -- 5.2 Two Separated Charged Conductive Spheres -- 5.3 Force Between Two Charged Spherical Conductors. , 5.4 A Charged Conductive Sphere and a Conductive Plate at Ground -- 5.5 Dielectric Sphere and Point Charge -- Problems -- Solutions -- References -- 6 Functions of Complex Variables and Electrostatics -- 6.1 Analytic Functions of Complex Variable -- 6.2 Electrostatics and Analytic Functions -- 6.3 The Function f left parenthesis z right parenthesis equals z Superscript muf(z)=zµ -- 6.3.1 The Quadrupole: f left parenthesis z right parenthesis equals z squaredf(z)=z2 -- 6.3.2 The Conductive Wedge at Fixed Potential -- 6.3.3 Edge of a Thin Plate -- 6.4 The Charged Wire: f left parenthesis z right parenthesis equals log zf(z)= logz -- Problems -- Solutions -- References -- 7 Conformal Mapping in Electrostatics -- 7.1 Conformal Mapping -- 7.2 Conformal Mapping and Harmonic Functions -- 7.3 Conformal Mapping and Bilinear Electrostatic Problems -- 7.3.1 Charged Wire Between Two Grounded Plates -- 7.4 The Linear-Fractional Function -- 7.4.1 The Split Cylinder: Two Opposite Half Cylinders at Different Potentials -- 7.5 The Schwarz-Christoffel Transformation -- 7.5.1 Conformal Transformation for a Single Corner -- 7.5.2 The Field Near the Edge of a Parallel-Plate Capacitor -- Problems -- Solutions -- References -- 8 Separation of Variables in Laplace Equation -- 8.1 The Method of Separation of Variables -- 8.2 Orthogonal and Complete Sets of Functions -- 8.3 Separation of Variables in the Laplace Equation -- 8.4 Separation of Variables in Cartesian Coordinates -- 8.4.1 Box with a Side at Given Potential and Five Conductive Grounded Sides -- 8.5 Separation of Variables in Spherical Coordinates with Azimuthal Symmetry -- 8.5.1 A Dielectric Sphere in a Uniform Electric Field -- 8.5.2 Potential for a Charged Ring -- 8.5.3 Conducting/Dielectric Sphere and Point Charge -- 8.6 Separation of Variables in Spherical Coordinates. , 8.7 Separation of Variables in Polar (Cylindrical) Coordinates -- 8.7.1 Wire and Cylindrical Capacitor -- 8.7.2 Conducting Wedge (Corner) -- 8.7.3 Split Cylinder -- 8.7.4 Cylinder in a Uniform Electric Field -- Problems -- Solutions -- References -- 9 Relativistic Transformation of E and B Fields -- 9.1 From Charge Invariance to the 4-Current Density -- 9.2 Electric Current in a Wire and a Charged Particle in Motion -- 9.3 Transformation of the E and B Fields -- 9.4 The Total Charge in Different Frames -- 9.5 Force Between Wires Carrying Currents -- 9.6 Electromagnetic Induction and Relative Motion of Circuits -- Problems -- Solutions -- References -- 10 Relativistic Covariance of Electrodynamics -- 10.1 Electrodynamics and Special Theory of Relativity -- 10.2 4-Vectors, Covariant and Contravariant Components -- 10.3 Relativistic Covariance of the Electrodynamics -- 10.4 4-Vector Potential and the Equations of Electrodynamics -- 10.5 The Continuity Equation -- 10.6 The Electromagnetic Tensor -- 10.7 Lorentz Transformation for Electric and Magnetic Fields -- 10.8 Maxwell Equations -- 10.8.1 Inhomogeneous Equations -- 10.8.2 Homogeneous Equations -- 10.9 Potential Equations -- 10.10 Gauge Transformations -- 10.11 Phase of the Wave -- 10.12 The Equations of Motion for a Charged Particle in the Electromagnetic Field -- References -- 11 Energy and Momentum of the Electromagnetic Field -- 11.1 Poynting's Theorem -- 11.2 Examples -- 11.2.1 Resistor -- 11.2.2 Solenoid -- 11.2.3 Capacitor -- 11.3 Energy Transfer in Electrical Circuits -- 11.4 Momentum Conservation in a System of Charges and Fields -- 11.5 The Maxwell Stress Tensor -- 11.6 Radiation Pressure on a Surface -- 11.7 Angular Momentum -- 11.8 The Covariant Maxwell Stress Tensor -- Problems -- Solutions -- References -- 12 The Feynman Paradox -- 12.1 The Paradox -- 12.2 A Charge and a Small Magnet. , 12.3 Analysis of the Angular Momentum Present in the System -- 12.4 Two Cylindrical Shells with Opposite Charge in a Vanishing Magnetic Field -- References -- 13 The Resonant Cavity -- 13.1 The Capacitor at High Frequency -- 13.2 The Resonant Cavity -- Problems -- Solutions -- References -- 14 Fields and Radiation -- 14.1 Fields of a Point Charge in Uniform Motion -- 14.1.1 Fields from the Lorentz Transformed Potentials for a Point Charge in Uniform Motion -- 14.2 Potentials and Fields for a Point Charge in Arbitrary Motion -- 14.2.1 The Retarded Potentials -- 14.2.2 Liénard-Wiechert Potentials -- 14.2.3 Comment to the Liénard-Wiechert Potentials -- 14.2.4 Covariant Form of the Liénard-Wiechert Potentials -- 14.2.5 Electric and Magnetic Fields -- 14.2.6 Calculation of the Electric and Magnetic Fields -- 14.3 Radiation by an Accelerated Charge -- 14.3.1 Radiation by a Charged Particle with Velocity v llc -- 14.3.2 Radiation by a Charged Particle with the Acceleration Parallel to the Velocity -- 14.3.3 Power Radiated by a Charged Particle in Arbitrary Motion -- 14.3.4 Radiation by a Charged Particle with the Acceleration Normal to the Velocity -- 14.4 Radiation Reaction -- 14.5 Electric Dipole Radiation -- Problems -- Solutions -- References -- 15 Test of the Coulomb's Law and Limits on the Mass of the Photon -- 15.1 Gauss's Law -- 15.2 First Tests of the Coulomb's Law -- 15.3 Proca Equations -- 15.4 The Williams, Faller and Hill Experiment -- 15.5 Limits from Measurements of the Magnetic Field of the Earth and of Jupiter -- 15.6 The Lakes Experiment -- 15.7 Other Measurements -- 15.8 Comments -- References -- 16 Magnetic Monopoles -- 16.1 Generalized Maxwell Equations -- 16.2 Generalized Duality Transformation -- 16.3 Symmetry Properties for Electromagnetic Quantities -- 16.4 The Dirac Monopole -- 16.5 Magnetic Field and Potential of a Monopole. , 16.6 Quantization Relation -- 16.7 Quantization from Electric Charge-Magnetic Pole Scattering -- 16.8 Properties of the Magnetic Monopoles -- 16.8.1 Magnetic Charge and Coupling Constant -- 16.8.2 Energy Losses for Monopoles in Matter -- 16.8.3 Magnetic Monopoles in Magnetic Field -- 16.9 Searches for Magnetic Monopoles -- 16.9.1 Detection of Magnetic Monopoles -- 16.9.2 Searches for Dirac Monopoles at Accelerators -- 16.9.3 Search for Cosmic Monopoles -- 16.9.4 Bounds on the Flux of Cosmic Magnetic Monopoles -- 16.9.5 Direct Searches for Cosmic Massive Monopoles -- References -- Appendix A Orthogonal Curvilinear Coordinates -- A.1 Orthogonal curvilinear coordinates -- A.2 Gradient -- A.3 Divergence -- A.4 Curl -- A.5 Laplacian -- A.6 Systems of Orthogonal Curvilinear Coordinates -- A.7 Spherical Coordinates -- A.8 Cylindrical Coordinates -- References -- Index.

Additional Edition: Print version: Lacava, Francesco Classical Electrodynamics Cham : Springer International Publishing AG,c2022 ISBN 9783031050985

Language: English