==Índice==
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* Abstract iii
* Chapter 1: Fundamental concepts 1
** Origin 1
** History 1
** Applications 3
** Requirements 5
** Limitations of the method 5
** Dealing with singularities 5
***Point charge type singularity 6
*** Step discontinuities 9
** Physical units and mathematical notation 10
** Organization of the book 11
* Chapter 2: Ellipsoids in Electric and Magnetic Fields 15
** Electric polarization 15
*** Basic equations 15
*** Permanent electric polarization 18
*** Induced electric polarization 20
*** Induced electric polarization of two interacting atoms 21
*** Dielectrics 24
** Magnetization 26
*** Basic equations 26
*** Permanent magnetization 28
*** Induced magnetization 29
** Conductors 30
*** Equivalent polarization 33
** Superconductors 34
*** Magnetization model 35
*** Surface conduction current model 36
** Summary of integro-differential equations 38
** Summary of induced polarization equations 39
** General formulation of the method 40
*** Solving the integro-differential equations by iteration 42
* Chapter 3: The depolarization tensor: basic treatment 45
** Definition 45
** General properties of '''''n''''' 47
*** Symmetric tensor 47
*** Trace 48
*** Orthogonal transformations 48
*** Symmetries 49
** '''''n''''' as a surface integral 50
** Surface step discontinuity 51
*** Surface charge density 51
*** Surface step discontinuity 52
** Calculation of '''''n''''' using electrostatic Gauss’s Law 54
*** Sheet of constant thickness and infinite extension 54
*** Right circular cylinder of infinite length 56
*** Sphere 58
** Other properties of the internal depolarization tensor '''''N(0)''''' 59
*** Integral expressions of the eigenvalues 59
*** Diagonalization and inversion 60
*** Infinite semiaxes and the inverse of '''''N(0)''''' 60
*** 'Invariance for similar ellipsoids 62
*** '''''N''''' is determined by aspect ratios 63
* Chapter 4: The depolarization tensor: advanced treatment 65
** Calculations of n from gravitational potentials 65
*** Triaxial ellipsoid 65
** Internal depolarization tensor N 67
*** Expressions with normal elliptic integrals E and F 67
*** N elliptic cylinder 68
*** N oblate spheroid 69
*** N prolate spheroid 74
*** Unified treatment of N for spheroids 77
*** Graphs of Na, Nb and Nc 79
**** Na 80
**** Nb 80
**** Nc 80
**** Combined graph 84
** External depolarization tensor 85
*** Obtention of the external gravitational potential by Ivory’s method 85
*** Near and far away point approximations to next 87
*** General expression of external n 87
**** Trace 90
**** Verificacion for the sphere 91
**** Elliptic cylinder 92
**** Oblate spheroid 95
**** Prolate spheroid 96
**** Triaxial ellipsoid 97
* Chapter 5: Energy, forces and cavities 99
** Thermodynamics of electrostatic and magnetostatic energy 99
*** Basic concepts 99
*** Thermodynamics of electromagnetism 101
** Anisotropy energy 103
** Origin of torques exerted on a body 105
** Torque exerted on an ellipsoid and the state of equilibrium 106
*** Dielectrics 106
**** Permanent polarization 106
**** Induced polarization 108
**** Anisotropic susceptibility 109
*** Magnetic materials 110
**** Permanent magnetization 110
**** nduced magnetization 111
**** Magnetic torque experiments 112
*** Conductors 112
*** Superconductors 113
** Force on an ellipsoid in a non-uniform field 114
** Infinite and infinitesimal bodies 114
** Cavities 116
*** Standard treatment 116
*** Some specific cavities: or homoeoids 117
*** Thin shells and the dipole layer 118
* Chapter 6: Selected problemas 121
** Dielectrics 121
*** Problem 01: Autoconsistent electric polarization of two atoms 121
*** Problem 02: Shape or crystalline anisotropy? 121
*** Problem 03: Dielectric sphere 122
*** Problem 04: Deriving n from the magnetic vector potential 124
*** Problem 05: Permanently magnetized infinite right circular cylinder 124
*** Problem 06: Isotropic magnetic sphere 126
** Conductors 126
*** Problem 07: Solve ellipsoidal conductors using equivalente polarization 126
*** Problem 08: A conductor is a perfect dielectric 127
*** Problem 09: Polarization of a spherical conductor 127
*** Problem 10: External field of a spherical conductor 128
*** Problem 11: Directions for which P is parallel to E0 in triaxial ellipsoids 129
*** Problem 12: Electric fields generated by sharp points 129
** Superconductors 130
*** Problem 13: Superconducting infinite cylinder and sheet 130
*** Problem 14: Magnetized superconducting sphere 130
*** Problem 15: Superconductivity as perfect diamagnetism 131
*** Problem 16: Magnetic moment of a superconducting ellipsoid 132
*** Problem 17: Description of Meissner Effect using magnetization currents 133
*** Problem 18: Approximate solution for non ellipsoidal bodies 133
** Depolarization tensor 133
*** Problem 19: Components of N in spherical symmetry 133
*** Problem 20: Single eigenvalue may determine the type of spheroid 134
*** Problem 21: Eigenvalues and aspect ratios 134
*** Problem 22: Sequence of ellipsoids over some aspect ratio curves 135
*** Problem 23: Eigenvalues of triaxial ellipsoids 135
*** Problem 24: Depolarization tensor of a very long right circular cylinder 136
*** Problem 25: Depolarization tensor of a sphere 136
*** Problem 26: Alternative way of obtaining certain eigenvalues of N 136
*** Problem 27: Solving the prolate spheroid with Legendre’s elliptic integrals 136
*** Problem 28: Spherical shell 137
*** Problem 29. Unit vector normal to the ellipsoid's surface 139
*** Problem 30: Surface step discontinuity of the depolarization tensor 139
*** Problem 31: Ellipsoidal conductor with net charge 140
*** Problem 32: Application of Ivory’s method to the sphere 140
*** Problem 33: Expression for far away fields obtained from next 141
*** Problem 34: Field on the external side of the surface of a polarized sphere 142
*** Problem 35: Microscopic origin of depolarization tensors 143
** Energy, forces and torques 143
*** Problem 36: Energy of a dielectric sphere 143
*** Problem 37: Fermi’s contact interaction 143
*** Problem 38: Torques on spheroids 144
*** Problem 39: Torque exerted over an anisotropic dielectric sphere 145
*** Problem 40: Torque on a magnetized disk 145
*** Problem 41: Torque on a very long superconducting right circular cylinder 146
*** Problem 42: Depolarization tensor of inifinitesimally thin shells 146
*** Problem 43: Applications of thin shells 146
* Appendix 1: Electromagnetic units 147
* Appendix 2: Vectorial Operators 151
* Appendix 3: Integral theorems of vector calculus 153
** Laplacian of a point charge’s potential 153
** Divergence, gradient and rotor theorems 155
** Extension of the divergence theorem 155
*** Point charge type singularities 156
*** Step discontinuities 157
**** Generalized divergence theorem 157
**** Generalized rotor theorem 158
**** Polarized bodies 158
* Appendix 4: Field of an electric dipole 161
** General expression 161
** Dipolar field's energy 162
* Appendix 5: Simmetries of the susceptibility tensors of single crystals 165
* Appendix 6: Dyadics 167
* Appendix 7: Ellipsoids 169
** Equations and main features 169
*** Equations, sections, volume and surface 169
*** Aspect ratios 170
** Normals to the surface and central distances 171
*** Summary of properties 173
** Confocal ellipsoids 174
*** Physical-geometric interpretation of κ 174
*** Corresponding points 175
* Appendix 8: Useful integrals 179
* Appendix 9: Legendre’s elliptic integrals 181
** Definitions 181
*** Notation used in the more important references 181
*** Special values and parametric graphs 182
*** Reduction to normal form of the elliptic integrals of interest 184
* Main references 187
* Alphabetic index 189
* About the author 193
==Sobre el autor==
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