Electromagnetism – Principles and Modern Applications: With Exercises And Solutions (1st Edition, 2024) by Christopher White

,by Lee Bong on 08/09/23. Re-use and distribution is strictly not permitted, except for Open Access articles.




Contents



Preface vii
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1. Why Electromagnetism? 1

2. Vector Algebra 5
2.1 Addition and Subtraction . . . . . . . . . . . . . . . . . . 5
2.2 Vector Components . . . . . . . . . . . . . . . . . . . . . . 7
2.3 The Dot Product . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 The Cross Product . . . . . . . . . . . . . . . . . . . . . . 12

3. Introducing Electricity 15
3.1 Electric Charge . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Coulomb’s Law . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 The Electric Field . . . . . . . . . . . . . . . . . . . . . . 19
3.4 Principle of Superposition . . . . . . . . . . . . . . . . . . 21
3.5 Field Lines . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.6 Electric Flux . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.7 Gauss’ Law . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.8 Electric Potential Energy . . . . . . . . . . . . . . . . . . 42
3.9 Electric Potential . . . . . . . . . . . . . . . . . . . . . . . 46
3.10 Conservative Fields . . . . . . . . . . . . . . . . . . . . . . 50
3.11 Superposition of Potential . . . . . . . . . . . . . . . . . . 52
3.12 Potential Energy of a System of Charges . . . . . . . . . . 53
3.13 Electric Field as the Gradient of Potential . . . . . . . . . 58



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4. A First Look at Circuits 63
4.1 Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Dielectrics . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3 Electric Current . . . . . . . . . . . . . . . . . . . . . . . . 70
4.4 Resistivity and Resistance . . . . . . . . . . . . . . . . . . 73
4.5 Electromotive Force and Circuits . . . . . . . . . . . . . . 75
by Lee Bong on 08/09/23. Re-use and distribution is strictly not permitted, except for Open Access articles.




4.6 Energy and Power in Circuits . . . . . . . . . . . . . . . . 82

5. Introducing Magnetism 85
5.1 The Magnetic Field . . . . . . . . . . . . . . . . . . . . . . 85
5.2 Magnetic Field Lines . . . . . . . . . . . . . . . . . . . . . 87
5.3 Magnetic Flux . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.4 Motion in a Magnetic Field . . . . . . . . . . . . . . . . . 90
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5.5 The Magnetic Field of a Moving Charge . . . . . . . . . . 92
5.6 The Biot–Savart Law . . . . . . . . . . . . . . . . . . . . . 93
5.7 Force on a Wire . . . . . . . . . . . . . . . . . . . . . . . . 96
5.8 Torque on a Current Loop . . . . . . . . . . . . . . . . . . 98
5.9 Ampère’s Law . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.10 Electromagnetic Induction . . . . . . . . . . . . . . . . . . 107
5.11 Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.12 Magnetic Energy . . . . . . . . . . . . . . . . . . . . . . . 114

6. A Second Look at Circuits 119
6.1 The R-C Circuit . . . . . . . . . . . . . . . . . . . . . . . 119
6.2 The R-L Circuit . . . . . . . . . . . . . . . . . . . . . . . . 123
6.3 The L-C Circuit . . . . . . . . . . . . . . . . . . . . . . . . 125
6.4 The L-R-C Circuit . . . . . . . . . . . . . . . . . . . . . . 128
6.5 Alternating Current . . . . . . . . . . . . . . . . . . . . . 131
6.6 The AC L-R-C Circuit . . . . . . . . . . . . . . . . . . . . 135

7. Maxwell’s Equations 139
7.1 The Displacement Current . . . . . . . . . . . . . . . . . . 139
7.2 Maxwell’s Equations . . . . . . . . . . . . . . . . . . . . . 142
7.3 The Divergence . . . . . . . . . . . . . . . . . . . . . . . . 144
7.4 The Curl . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.5 Maxwell Equations in Differential Form . . . . . . . . . . 153
7.6 Electromagnetic Waves . . . . . . . . . . . . . . . . . . . . 156

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7.7 The Poynting Vector . . . . . . . . . . . . . . . . . . . . . 162
7.8 Polarisation . . . . . . . . . . . . . . . . . . . . . . . . . . 163

8. Relativity and Maxwell’s Equations 169
8.1 Relativistic Kinematics . . . . . . . . . . . . . . . . . . . . 170
8.2 Four Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . 172
by Lee Bong on 08/09/23. Re-use and distribution is strictly not permitted, except for Open Access articles.




8.3 The Dot Product for 4-Vector . . . . . . . . . . . . . . . . 177
8.4 The Metric Tensor . . . . . . . . . . . . . . . . . . . . . . 179
8.5 The Velocity 4-Vector . . . . . . . . . . . . . . . . . . . . 181
8.6 Tensors and Relativistic Equations . . . . . . . . . . . . . 183
8.7 The 4-Potential and Field Strength . . . . . . . . . . . . . 185
8.8 The 4-Vector Current Density . . . . . . . . . . . . . . . . 189
8.9 The Covariant Maxwell Equations . . . . . . . . . . . . . 191
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9. Maxwell’s Equations from Symmetry 199
9.1 The Need for Quantum Field Theory . . . . . . . . . . . . 199
9.2 Matter and the Dirac Equation . . . . . . . . . . . . . . . 202
9.3 Global Gauge Invariance . . . . . . . . . . . . . . . . . . . 203
9.4 Local Gauge Invariance . . . . . . . . . . . . . . . . . . . 204
9.5 Gauge Invariance and the Other Forces . . . . . . . . . . . 209

10. The Double Copy: From Electromagnetism to Gravity 213
10.1 Scattering Amplitudes in QFT . . . . . . . . . . . . . . . 214
10.2 Gravity and General Relativity . . . . . . . . . . . . . . . 219
10.3 The Double Copy for Scattering Amplitudes . . . . . . . . 223
10.4 The Double Copy for Classical Solutions . . . . . . . . . . 225

Appendix A Line and Surface Integrals 231
A.1 Line Integrals . . . . . . . . . . . . . . . . . . . . . . . . . 231
A.2 Surface Integrals . . . . . . . . . . . . . . . . . . . . . . . 236

Appendix B The Dirac Equation 243

Appendix C Solutions to Exercises 249

Index 271