These lecture notes cover classical electrodynamics at the level of advanced undergraduates or postgraduates. There is a strong emphasis on the general features of the electromagnetic field and, in particular, on the properties of electromagnetic radiation. It offers a comprehensive and detailed, as well as self-contained, account of material that can be covered in a one-semester course for students with a solid undergraduate knowledge of basic electricity and magnetism.

Preface vii

Glossary xiii

1. Maxwell’s Equations 1

1.1 Review of familiar basics 1

1.2 Continuity equation; conservation of charge 2

1.3 Potentials, gauge invariance; radiation gauge, Lorentz gauge 3

1.4 Force, work, energy conservation 6

1.5 Conservation of momentum 8

1.6 Conservation of angular momentum 11

1.7 Virial theorem 12

2. Electromagnetic Pulses 15

2.1 Conserved energy, momentum, angular momentum 15

2.2 Energy velocity, momentum velocity 16

2.3 Unidirectional pulses 20

3. Lorentz Transformation 23

3.1 Coordinate transformation, 4-vector, 4-dyadic 23

3.2 Infinitesimal transformations; rapidity 25

3.3 Transformation laws for fields 27

3.4 4-columns, 4-rows 32

3.5 Finite Lorentz transformations 41

3.6 A digression: Dirac’s magnetic monopole 45

4. 3+1–Dimensional Notation 49

4.1 Contravariant and covariant components 49

4.2 Field dyadic; energy-momentum dyadic 52

4.3 Wave 4-vector; 4-velocity; Doppler effect 56

5. Action, Reaction — Interaction 61

5.1 Action principles of classical mechanics 61

      5.1.1 Lagrange’s formulation 61

      5.1.2 Hamilton’s formulation 63

      5.1.3 Schwinger’s formulation 64

      5.1.4 Velocity-dependent forces 65

5.2 Lagrange function of the electromagnetic field 68

5.3 Particles and fields in interaction 71

5.4 Disposing of the gauge-dependent terms 71

6. Retarded Potentials 75

6.1 Green’s function 75

6.2 Li´enard–Wiechert potentials 80

6.3 Retarded time 80

7. Radiation Fields 85

7.1 Far fields 85

7.2 Emitted power 89

7.3 Larmor formula 92

7.4 Longitudinal and transverse components of a field 95

7.5 Charge point of view 98

7.6 Simple model antenna 102

8. Spectral Properties of Radiation 107

8.1 Fourier-transformed fields 107

8.2 Spectral distribution 110

8.3 Dipole approximation 112

8.4 Impulsive scattering 114

8.5 Bremsstrahlung 117

9. Time-Dependent Spectral Distribution 119

9.1 Time-dependent power spectrum 119

9.2 Constant acceleration 120

9.3 Cherenkov radiation 124

10. Synchrotron Radiation 129

10.1 Kinematics 129

10.2 Time-dependent spectrum 131

10.3 Total radiated power . 133

10.4 Power emitted into the mth harmonic 138

10.5 High harmonics 144

10.6 “Roll over” 146

10.7 Polarization 148

10.8 Angular distribution 153

10.9 Qualitative picture 155

11. Scattering 157

11.1 Thomson scattering 157

11.2 Rayleigh scattering 159

12. Diffraction 165

12.1 Encounter with Huygens’s principle 165

12.2 Large apertures 169

12.3 Single large circular aperture 170

      12.3.1 Differential cross section 170

      12.3.2 Total cross section 171

      12.3.3 Small diffraction angles 173

12.4 Induced surface currents 175

12.5 Large obstacles 176

12.6 Poisson’s spot 178

      12.6.1 Bright center in the shadow 178

      12.6.2 Size of the bright center 180

      12.6.3 Central intensity behind a long strip 183

12.7 Diffraction at a straight edge 185

      12.7.1 Transition region 186

      12.7.2 Exact solution 188

Exercises with Hints 197

Exercises for Chapters 1–12 197

Hints 217

Electromagnetic Units 227

Index 231

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