(ebook Physics) - Electro magnetic field theory

(ebook Physics) - Electro magnetic field theory - ELECTRO...

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ELECTRO MAGNETIC FIELD THEORY Υ Bo Thidé U P S I L O N M E D I A
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Bo Thidé E LECTROMAGNETIC F IELD T HEORY
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Also available E LECTROMAGNETIC F IELD T HEORY E XERCISES by Tobia Carozzi, Anders Eriksson, Bengt Lundborg, Bo Thidé and Mattias Waldenvik
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E LECTROMAGNETIC F IELD T HEORY Bo Thidé Swedish Institute of Space Physics and Department of Astronomy and Space Physics Uppsala University, Sweden Υ U P S I L O N M E D I A · U P P S A L A · S W E D E N
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This book was typeset in L A T E X 2 ε on an HP9000/700 series workstation and printed on an HP LaserJet 5000GN printer. Copyright ©1997, 1998, 1999 and 2000 by Bo Thidé Uppsala, Sweden All rights reserved. Electromagnetic Field Theory ISBN X-XXX-XXXXX-X
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Contents Preface xi 1 Classical Electrodynamics 1 1.1 Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Coulomb’s law . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 The electrostatic field . . . . . . . . . . . . . . . . . . 2 1.2 Magnetostatics . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Ampère’s law . . . . . . . . . . . . . . . . . . . . . . 4 1.2.2 The magnetostatic field . . . . . . . . . . . . . . . . . 6 1.3 Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.1 Equation of continuity . . . . . . . . . . . . . . . . . 9 1.3.2 Maxwell’s displacement current . . . . . . . . . . . . 9 1.3.3 Electromotive force . . . . . . . . . . . . . . . . . . . 10 1.3.4 Faraday’s law of induction . . . . . . . . . . . . . . . 11 1.3.5 Maxwell’s microscopic equations . . . . . . . . . . . 14 1.3.6 Maxwell’s macroscopic equations . . . . . . . . . . . 14 1.4 Electromagnetic Duality . . . . . . . . . . . . . . . . . . . . 15 Example 1.1 Duality of the electromagnetodynamic equations 16 Example 1.2 Maxwell from Dirac-Maxwell equations for a fixed mixing angle . . . . . . . . . . . . . . . 17 Example 1.3 The complex field six-vector . . . . . . . . 18 Example 1.4 Duality expressed in the complex field six-vector 19 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2 Electromagnetic Waves 23 2.1 The wave equation . . . . . . . . . . . . . . . . . . . . . . . 24 2.1.1 The wave equation for E . . . . . . . . . . . . . . . . 24 2.1.2 The wave equation for B . . . . . . . . . . . . . . . . 24 2.1.3 The time-independent wave equation for E . . . . . . 25 2.2 Plane waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.1 Telegrapher’s equation . . . . . . . . . . . . . . . . . 27 i
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ii CONTENTS 2.2.2 Waves in conductive media . . . . . . . . . . . . . . . 29 2.3 Observables and averages . . . . . . . . . . . . . . . . . . . . 30 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3 Electromagnetic Potentials 33 3.1 The electrostatic scalar potential . . . . . . . . . . . . . . . . 33 3.2 The magnetostatic vector potential . . . . . . . . . . . . . . . 34 3.3 The electromagnetic scalar and vector potentials . . . . . . . . 34 3.3.1 Electromagnetic gauges . . . . . . . . . . . . . . . . 36 Lorentz equations for the electromagnetic potentials . 36 Gauge transformations . . . . . . . . . . . . . . . . . 36 3.3.2 Solution of the Lorentz equations for the electromag- netic potentials . . . . . . . . . . . . . . . . . . . . . 38 The retarded potentials . . . . . . . . . . . . . . . . . 41 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4 The Electromagnetic Fields 43 4.1 The magnetic field . . . . . . . . . . . . . . . . . . . . . . . 45 4.2 The electric field . . . . . . . . . . . . . . . . . . . . . . . . 47 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5 Relativistic Electrodynamics 51 5.1 The special theory of relativity . . . . . . . . . . . . . . . . . 51 5.1.1 The Lorentz transformation . . . . . . . . . . . . . . 52 5.1.2 Lorentz space . . . . . . . . . . . . . . . . . . . . . . 53 Metric tensor . . . . . . . . . . . . . . . . . . . . . . 54 Radius four-vector in contravariant and covariant form 54 Scalar product and norm . . . . . . . . . . . . . . . . 55 Invariant line element and proper time . . . . . . . . . 56 Four-vector fields . . . . . . . . . . . . . . . . . . . . 57 The Lorentz transformation matrix . . . . . . . . . . . 57 The Lorentz group . . . . . . . . . . . . . . . . . . . 58 5.1.3 Minkowski space . . . . . . . . . . . . . . . . . . . . 58 5.2 Covariant classical mechanics . . . . . . . . . . . . . . . . . 61 5.3 Covariant classical electrodynamics . . . . . . . . . . . . . . 62 5.3.1 The four-potential . . . . . . . . . . . . . . . . . . . 62 5.3.2 The Liénard-Wiechert potentials . . . . . . . . . . . . 63 5.3.3 The electromagnetic field tensor . . . . . . . . . . . . 65 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Downloaded from http://www.plasma.uu.se/CED/Book Draft version released 13th November 2000 at 22:01.
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iii 6 Interactions of Fields and Particles 69 6.1 Charged Particles in an Electromagnetic Field . . . . . . . . . 69 6.1.1 Covariant equations of motion . . . . . . . . . . . . . 69 Lagrange formalism . . . . . . . . . . . . . . . . . . 69 Hamiltonian formalism . . . . . . . . . . . . . . . . . 72 6.2 Covariant Field Theory .
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(ebook Physics) - Electro magnetic field theory - ELECTRO...

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