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El. knyga: Core Electrodynamics

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This book is intended to engage the students in the elegance of electrodynamics and special relativity, whilst giving them the tools to begin graduate study. Here, from the basis of experiment, the authors first derive the Maxwell equations and special relativity. Introducing the mathematical framework of generalized tensors, the laws of mechanics, Lorentz force and the Maxwell equations are then cast in manifestly covariant form. This provides the basis for graduate study in field theory, high energy astrophysics, general relativity and quantum electrodynamics. As the title suggests, this book is “electrodynamics lite”. The journey through electrodynamics is kept as brief as possible, with minimal diversion into details, so that the elegance of the theory can be appreciated in a holistic way. It is written in an informal style and has few prerequisites; the derivation of the Maxwell equations and their consequences is dealt with in the first chapter. Chapter 2 is devoted to conservation equations in tensor formulation; here, Cartesian tensors are introduced. Special relativity and its consequences for electrodynamics are introduced in Chapter 3 and cast in four-vector form, and here, the authors introduce generalized tensors. Finally, in Chapter 4, Lorentz frame invariant electrodynamics is developed. Supplementary material and examples are provided by the two sets of problems. The first is revision of undergraduate electromagnetism, to expand on the material in the first chapter. The second is more advanced corresponding to the remaining chapters, and its purpose is twofold: to expand on points that are important, but not essential, to derivation of manifestly covariant electrodynamics, and to provide examples of manipulation of cartesian and generalized tensors. As these problems introduce material not covered in the text, they are accompanied by full worked solutions. The philosophy here is to facilitate learning by problem solving, as well as by studying the text. Extensive appendices for vector relations, unit conversion and so forth are given with graduate study in mind. 
1 A Brief Tour of Electromagnetism
1(20)
1.1 The Building Blocks
1(2)
1.2 Maxwell I and II
3(9)
1.2.1 Flux of a Vector Field
5(1)
1.2.2 Flux of E
6(4)
1.2.3 Flux of B
10(1)
1.2.4 Conservative and Nonconservative Fields
11(1)
1.3 Maxwell III and IV
12(6)
1.3.1 Faraday's Law and Galilean In variance
13(3)
1.3.2 Ampere's Law and Conservation of Charge
16(2)
1.4 Electromagnetic Waves
18(1)
1.5 Conservation Equations
19(2)
2 Field Energy and Momentum
21(16)
2.1 Tensors and Conservation Equations
22(6)
2.1.1 Momentum Flux Density Tensor
22(2)
2.1.2 Momentum Flux, Gas Pressure and Fluid Equations
24(2)
2.1.3 Cartesian Tensors, Some Definitions
26(2)
2.2 Field Momentum and Maxwell Stress
28(5)
2.2.1 Energy Conservation: Poynting's Theorem
29(1)
2.2.2 Momentum Conservation: Maxwell Stress
30(3)
2.3 Radiation Pressure
33(4)
3 A Frame Invariant Electromagnetism
37(22)
3.1 The Lorentz Transformation
38(4)
3.2 The Moving Charge and Wire Experiment
42(4)
3.3 Maxwell in Terms of Potentials
46(1)
3.4 Generalized Coordinates
47(4)
3.5 Four Vectors and Four Vector Calculus
51(4)
3.5.1 Some Mechanics, Newton's Laws
51(3)
3.5.2 Some Four Vector Calculus
54(1)
3.6 A Frame Invariant Electromagnetism
55(4)
3.6.1 Charge Conservation
55(1)
3.6.2 A Manifestly Covariant Electromagnetism
56(3)
4 The Field Tensors
59(18)
4.1 Invariant Form for E and B: the EM Field Tensor
59(3)
4.2 Maxwell's Equations in Invariant Form
62(3)
4.3 Conservation of Energy-Momentum
65(1)
4.4 Lorentz Force
66(2)
4.4.1 Manifestly Covariant Electrodynamics
67(1)
4.5 Transformation of the Fields
68(1)
4.6 Field from a Moving Point Charge
69(3)
4.7 Retarded Potential
72(5)
Suggested Texts 77(2)
Appendix A Revision Problems 79(6)
Appendix B Solutions to Revision Problems 85(12)
Appendix C Some Advanced Problems 97(4)
Appendix D Solution to Advanced Problems 101(12)
Appendix E Vector Identities 113(4)
Appendix F Tensors 117(6)
Appendix G Units and Dimensions 123(2)
Appendix H Dimensions and Units 125(4)
Appendix I Physical Constants (SI) 129(2)
Index 131
Sandra Chapman is primarily but not exclusively a plasma physicist working on non-linear and complex systems in astrophysics and in the laboratory. She is Professor of Physics and Director of the Centre for Fusion, Space and Astrophysics at the University of Warwick. She read Physics on an Exhibition Scholarship to Imperial College, London and her interest in nonlinear systems began with her PhD work (also at Imperial College). Her early work was recognised with the COSPAR Zeldovich Medal (commission D) and the EGS Young Scientists' Medal. She was selected to give the 2014 Royal Astronomical Society James Dungey Lecture and the Ed Lorenz Lecture for the 2020 Fall Meeting of the American Geophysical Union. Sandra was a 2017/18 Fulbright-Lloyd's of London Scholar, a 2003/4 Fellow at the Radcliffe Institute for Advanced Study Harvard and has also been granted Research Fellowships by the Nuffield Foundation and the Japan Society for the Promotion of Science. She has published over 180 papers in the refereed literature. She is also an artist who works to bridge the arts- science divide and has held a NESTA Dreamtime fellowship working as an artist with the British Antarctic Survey in Antarctica.
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