This book examines the topics of magnetohydrodynamics and plasma oscillations, in addition to the standard topics discussed to cover courses in electromagnestism, electrodynamics, and fundamentals of physics, to name a few. This textbook on electricity and magnetism is primarily targeted at graduate students of physics. The undergraduate students of physics also find the treatment of the subject useful. The treatment of the special theory of relativity clearly emphasises the Lorentz covariance of Maxwell's equations. The rather abstruse topic of radiation reaction is covered at an elementary level, and the Wheeler–Feynman absorber theory has been dwelt upon briefly in the book.
Author(s): Amal Kumar Raychaudhuri
Series: Texts and Readings in Physical Sciences 21
Edition: 1
Publisher: Springer Nature Singapore
Year: 2022
Language: English
Pages: 300
City: Singapore
Tags: electrostatics, magnetism, Gauss' theorem, Laplace equation, Poisson equation, multipole moments, dielectrics and uniqueness theorem, field energy, magnetic fields, electromagnetic induction, Maxwell's equations, electromagnetic waves, wave guide and cavity resonators, anisotropic media, radiation field, moving charged particle, magnetohydrodynamics, plasma oscillations, relativity
Foreword to the Revised Edition
Preface
Contents
About the Author
1 Empirical Basis of Electrostatics
1.1 The Idea of Electric Charge
1.2 The Law of Interaction of Point Charges
2 Direct Calculation of Field in Some Cases
2.1 Interaction Between Dipoles
2.2 Potential due to Surface Distribution of Charges and Dipoles
2.3 The Dirac δ-Function
3 Gauss' Theorem, Laplace and Poisson Equations
3.1 Equations of Laplace and Poisson
3.1.1 Green's Theorem in Vector Calculus
3.1.2 A Formula of Interest in Field Theory
3.1.3 Earnshaw's Theorem
4 Analysis of the Electrostatic Field: Multipole Moments
4.1 Energy of Multipoles in an External Field
5 Dielectrics and the Uniqueness Theorem
5.1 Boundary Conditions to be Satisfied at the Interface of Two Different Dielectrics
5.2 The Uniqueness Theorem
5.3 Field in a Cavity in a Dielectric
5.4 Molecular Polarizability and Clausius-Mossotti Relation
6 Solution of the Laplace Equation
6.1 Rectangular Cartesian Coordinates
6.2 Cylindrical Polar Coordinates
6.3 Method of Electrical Images
6.3.1 A Point Charge in Front of an Infinite Conducting Plane
6.3.2 Conducting Sphere
6.3.3 Two Spheres Intersecting at Right Angle
6.4 Green's Function Method
6.5 Method Using Complex Variables
7 Field Energy and Forces in Electrostatics
7.1 Electrostriction
7.2 Pressure Discontinuity at the Boundary of a Dielectric
7.3 Force Sucking in a Dielectric into a Capacitor
7.4 Force on the Surface of a Charged Conductor
8 Stationary Currents and Magnetic Fields
8.1 Magnetic Moment or a Current Distribution
8.2 Relation Between Magnetic Moment and Angular Momentum for a Classical System
8.2.1 Larmor Precession
8.3 Permanent Magnets and the Vector H
8.4 Boundary Conditions at the Interface of Two Media
8.5 Scalar and Vector Potentials for a Static Magnetic Field
8.6 Uniformly Magnetized Sphere
9 Electromagnetic Induction and Energy of the Magnetic Field
9.1 Law of Induction in a Moving Coil or Medium
9.2 Energy of the Magnetostatic Field
9.3 Calculation of Self and Mutual Inductances
9.4 Current in Circuits with Inductance, Resistance and Capacitance
9.4.1 The Case of an Alternating Impressed Electromotive Force
10 Maxwell's Equations, Electromagnetic Energy and Momentum
10.1 The Electromagnetic Waves in an Isotropic Homogeneous Dielectric
10.2 Energy Flux and the Poynting Vector
10.3 The General Stress Tensor and Momentum of Radiation
10.4 The Pressure of Radiation
11 Reflection and Refraction of Electromagnetic Waves
11.1 Total Internal Reflection
11.2 Reflection at Conducting Surfaces (Metallic Reflection)
12 Wave Guides and Cavity Resonators
12.1 Transverse Electromagnetic Waves (TEM Waves)
12.2 TM and TE Modes
12.3 Energy Flux, Attenuation in Wave Guides and Q of Cavities
12.3.1 Rectangular Transverse Section
12.3.2 Circular Cylindrical Cavity
13 Electromagnetic Waves in Anisotropic Media
13.1 The Relation Between the Directions of D, B, k, etc.
13.2 The Relation Between the Vectors in the Two Waves with the Same Wave Normal
13.3 Crystal Classes and Optic Axes
13.4 Conical Refraction
13.5 External Conical Refraction
14 Solution of Maxwell's Equations: Retarded and Advanced Potentials
14.1 The Near Field and the Far Field
15 Analysis of the Radiation Field
15.1 The Hertz Vector and Hertz's Method of Analysis
16 Field Due to a Moving Charged Particle
16.1 Field of a Particle in Uniform Rectilinear Motion
16.2 The Method of Virtual Quanta
16.3 Number of Equivalent Photons in the Virtual Radiation Field
17 Field of a Particle in Non-Uniform Motion
17.1 Radiation from a Particle Describing a Circular Orbit with Uniform Velocity—Acceleration Always Orthogonal to the Velocity
17.2 Classical Theory of Bremsstrahlung
18 Electrons in Material Media
18.1 Cerenkov Radiation
18.2 Scattering of Electromagnetic Waves by Electrons
18.3 Dispersion and Absorption
19 Motion of Charged Particles in Electromagnetic Fields
19.1 Weak Perturbations and Drift of the Guiding Centre
19.2 Slow Temporal Variation of Magnetic Field—Adiabatic Invariants
19.3 Confinement of Charged Particles in Non-homogeneous Magnetic Fields—The Magnetic Bottle and Magnetic Mirror
20 Magnetohydrodynamics—Conducting Fluids and Magnetic Fields
20.1 Stationary Solutions of the Magneto-Hydrodynamic Equations
20.2 The Pinch Effect
20.3 Instability of the Cylindrical Plasma
20.4 The Magneto-Hydrodynamic Waves
20.5 Dissipative Effects
21 Two Component Plasma Oscillations
21.1 Waves in the Plasma
22 The Theory of the Electron
22.1 Critique of the Classical Theory
22.2 The Radiation Reaction
22.3 The Wheeler–Feynmann Absorber Theory of the Radiation Reaction
23 Special Theory of Relativity and Electromagnetism
23.1 The Lorentz Transformation Formulae
23.2 Covariant and Contravariant Vectors and Tensors
23.3 Variation of Mass with Velocity
23.4 Tensor Form of the Equation of Electromagnetism
24 Variational Principle Formulation of Maxwell's Equations and Lagrangian Dynamics of Charged Particles in Electromagnetic Fields
24.1 Lagrangian and Hamiltonian of a Charged Particle in an Electromagnetic Field
Appendix A Index
Index
