Classical electrodynamics : from image charges to the photon mass and magnetic monopoles / / Francesco Lacava

• Record Nr.: UNISA996495165203316
• Autore: Lacava Francesco
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 9783031050992; 9783031050985
• Edizione: [Second edition.]
• Descrizione fisica: 1 online resource (379 pages)
• Collana: Undergraduate lecture notes in physics
• Disciplina: 537.6
• Soggetti: Electrodynamics; Microwaves; Optics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.