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<p>Preface ix</p> <p><b>Chapter 1 Magnetic Field 1</b></p> <p>1.1 Overview of history 1</p> <p>1.2 Magnetic fields and magnetic forces 6</p> <p>1.2.1 First experiments 7</p> <p>1.2.2 Topography: invariances and symmetries 8</p> <p>1.3 Magnetic fields created by currents 11</p> <p>1.3.1 Magnetic field created by a volume current distribution 11</p> <p>1.3.2 Magnetic field created by a surface current distribution or by a filiform current element 12</p> <p>1.4 Biot–Savart experiment 13</p> <p>1.5 From field B to vector potential A 14</p> <p>1.6 Symmetry and invariance properties of the magnetic field related to the symmetry and invariances of the current distribution 15</p> <p>1.6.1 Distribution of currents having a plane of symmetry 17</p> <p>1.6.2 Current distribution and anti-symmetry plane 17</p> <p>1.6.3 Invariance 18</p> <p>1.7 Calculation of the magnetic field (principle of) 20</p> <p>1.7.1 Examples of field calculations 20</p> <p>1.8 Circulation properties of B Ampère’s theorem 36</p> <p>1.8.1 Integral form of Ampère’s theorem 37</p> <p>1.8.2 Local form of Ampère’s theorem 43</p> <p>1.9 Magnetic field flux conservation – vector potential 43</p> <p>1.9.1 Local relationship 43</p> <p>1.9.2 Integral relationship – magnetic flux 44</p> <p>1.9.3 Potential vector of the magnetic field 45</p> <p>1.10 Transit relationships 52</p> <p>1.10.1 Circulation property of B Discontinuity of the tangential component of B 53</p> <p>1.10.2 Flow property of B Continuity of the normal component of B 55</p> <p><b>Chapter 2 Magnetic Forces and their Work 57</b></p> <p>2.1 Introduction: Academy of Sciences 57</p> <p>2.2 Action of a magnetic field on a circuit through which a current flows 59</p> <p>2.2.1 Ampère/Laplace force 59</p> <p>2.3 Current in a conductor subjected to an electromagnetic field 63</p> <p>2.3.1 Examples: action of a rectilinear wire, through which a current flows on another rectilinear wire 63</p> <p>2.4 Local Ohm’s law 64</p> <p>2.5 Hall effect 65</p> <p>2.5.1 Hall effect applications (Figure 2.9) 67</p> <p>2.6 Ampère/Laplace magnetic forces on a conductor (Figures 2.10 and 2.11) 68</p> <p>2.6.1 Ampère definition 72</p> <p>2.7 Work of electromagnetic forces 72</p> <p>2.7.1 Cut-off flow theorem 73</p> <p>2.7.2 Case of a closed circuit through which a constant current I flows: Maxwell’s theorem 73</p> <p>2.8 Application to the study of torsor of magnetic forces exerted by an invariable field on a rigid circuit 80</p> <p>2.9 Potential energy 81</p> <p>2.9.1 Case of a transverse displacement 82</p> <p>2.9.2 Case of a rotation 83</p> <p>2.10 Example: flux of a turn in a magnetic field 84</p> <p>2.10.1 Turn in a transverse displacement 84</p> <p>2.10.2 Turn in rotation 85</p> <p>2.11 Potential energy of interaction with a magnetic field: magnetic dipole 86</p> <p>2.11.1 Magnetic force and moment acting on the loop 88</p> <p>2.12 Electrostatic/magnetostatic analogy 89</p> <p><b>Chapter 3 Magnetic Media 91</b></p> <p>3.1 Introduction: orbital and spin magnetic moments 91</p> <p>3.2 Experimental studies 93</p> <p>3.3 Microscopic origins of magnetism: basic concepts 95</p> <p>3.3.1 Diamagnetism 95</p> <p>3.3.2 Paramagnetism 96</p> <p>3.3.3 Ferromagnetism 98</p> <p>3.4 Macroscopic appearance; magnetization intensity 100</p> <p>3.4.1 Diamagnetic and paramagnetic materials 101</p> <p>3.5 Determining the magnetic field created by a magnetized medium 101</p> <p>3.5.1 Vector potential of a closed circuit, at a point in the vacuum 103</p> <p>3.6 Macroscopic aspects; magnetization currents 104</p> <p>3.6.1 Total magnetic field in the presence of magnetic media 108</p> <p>3.6.2 General equations of magnetostatics in the presence of magnetized media 109</p> <p>3.7 Generalized Ampère’s theorem: magnetic excitation 110</p> <p>3.7.1 Transit relationships 111</p> <p>3.8 Perfect magnetic media or HLI media – homogeneous, linear, isotropic (Figure 3.21) 113</p> <p>3.8.1 Definition 113</p> <p>3.9 Magnetic field equations for perfect materials and vacuum 116</p> <p>3.9.1 Hysteresis loop 118</p> <p>3.9.2 Applications 121</p> <p><b>Chapter 4 Induction 123</b></p> <p>4.1 Introduction: variable regimes 123</p> <p>4.2 Properties of electrical induction and magnetic field 127</p> <p>4.3 Phenomenon of electromagnetic induction 127</p> <p>4.3.1 Faraday–Lenz law 130</p> <p>4.3.2 Terminology and classification of induction phenomena 132</p> <p>4.3.3 Static or Neumann induction and motional or Lorentz induction 136</p> <p>4.3.4 Motional or Lorentz induction 140</p> <p>4.4 Different inductions 149</p> <p>4.4.1 Auto-induction electromotive force 149</p> <p>4.4.2 Mutual inductance – coupling coefficient 150</p> <p>4.5 Applications 154</p> <p>4.6 Electromechanical conversion; moving bar in a uniform B-field 154</p> <p>4.6.1 We place ourselves in the laboratory repository 154</p> <p>4.6.2 We place ourselves in the frame of reference to the bar 156</p> <p>4.7 Vector potential and quantum mechanics 157</p> <p>4.8 Appendix: another example of an induction problem 170</p> <p>4.8.1 Coil with tube-shaped conductive core 170</p> <p><b>Chapter 5 Propagation: Special Relativity 179</b></p> <p>5.1 Introduction 179</p> <p>5.1.1. Potential of a moving charge: general solution by Liénard and Wiercherts 180</p> <p>5.1.2 Spherical waves 182</p> <p>5.2 Light and electromagnetic waves 184</p> <p>5.2.1 Spherical wave from a point source 186</p> <p>5.2.2 Paradox of advanced actions 189</p> <p>5.3 Relativity 195</p> <p>5.3.1 Galileo’s relativity 195</p> <p>5.3.2 Special relativity 196</p> <p>5.3.3 Charges in motion: from “Coulomb” to “Ampère” 217</p> <p>5.3.4 Note on Lorentz equations 225</p> <p>Conclusion 227</p> <p>Appendices 229</p> <p>Appendix 1 Ampère/Laplace Magnetic Actions Undergone by a Current Loop Placed in an External Magnetic Field 231</p> <p>Appendix 2 Magnetostatic Potential Energy of a Current System (Perfect Media) 241</p> <p>Appendix 3 Operator Expressions in Cartesian Coordinates 249</p> <p>Appendix 4 Some Key Players in Electromagnetism and Special Relativity 261</p> <p>References 277</p> <p>Index 279</p>

<p><b>Christian Gontrand</b> is a professor at INL/INSA Lyon, France, focusing on 3D circuits. He was formerly a head professor in the Smart Power Integration team at AMPERE lab and had the technical charge of the CIMIRLY from 1988 to 1996.</p>

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