What is included with this book?
Introduction | p. xiii |
Acknowledgments | p. xv |
List of Symbols | p. xvii |
Magnetic Field in a Nonmagnetic Medium | |
Interaction of Constant Currents and Ampere's Law | p. 1 |
Magnetic Field of Constant Currents | p. 3 |
General form of Biot-Savart law | p. 5 |
The Vector Potential of the Magnetic Field | p. 8 |
Magnetic Field and Vector Potential, Caused by Linear and Surface Currents | p. 12 |
Magnetic field of a current filament | p. 13 |
The vector potential A and the magnetic field B of the current in a circular loop | p. 15 |
The magnetic field of a magnetic dipole | p. 18 |
The vector potential of a system of dipoles | p. 21 |
Behavior of the of field B near surface currents | p. 22 |
System of Equations of the Magnetic Field B Caused by Conduction Currents | p. 25 |
Example one: magnetic field due to a current in a cylindrical conductor | p. 29 |
Example two: magnetic field of an infinitely long solenoid | p. 31 |
Example three: magnetic field of a current toroid | p. 34 |
The System of Equations for Vector Potential A | p. 36 |
Magnetic Field Caused by Magnetization Currents | |
Magnetization Currents and Magnetization: Biot-Savart Law | p. 39 |
System of Equations of the Field B in the Presence of a Magnetic Medium | p. 41 |
Relation between magnetization Currents and Magnetization | p. 42 |
System of Equations with Respect to the Magnetic Field B | p. 45 |
Field H and Relationship between Vectors B, P, and H | p. 46 |
Three Types of Magnetic Media and their Magnetic Parameters | p. 47 |
Inductive and residual magnetization | p. 47 |
Types of magnetic medium | p. 48 |
Magnetic permeability | p. 49 |
System of Equations for the Magnetic Field B | p. 50 |
Distribution of Magnetization Currents | p. 51 |
Volume density | p. 51 |
Surface density | p. 53 |
System of Equations for the Fictitious Field H and Distribution of its Generators | p. 55 |
Volume density | p. 55 |
Surface density | p. 56 |
Difference between the Fields B and H | p. 56 |
Example 1: Current loop in a homogeneous medium | p. 57 |
Example 2: Uniform fields B and H in a medium with one plane interface | p. 57 |
Example 3: Fields B and H inside the toroid with a small gap | p. 59 |
Example 4: Fields B and H inside the solenoid | p. 61 |
Example 5: Fields B and H inside the magnetic solenoid | p. 61 |
Example 6: Influence of a thin magnetic shell | p. 61 |
The System of Equations for the Fields B and H in Special Cases | p. 62 |
Case 1: A nonmagnetic medium | p. 62 |
Case 2: Conduction currents are absent | p. 63 |
Case 3: Residual magnetization and conduction currents are absent | p. 64 |
Case 4: Uniform piece-wise medium where conduction current and residual magnetization are absent | p. 65 |
Magnetic Field in the Presence of Magnetic Medium | |
Solution of the Forward Problem in a Piece-Wise Uniform Medium When Conduction Currents and Residual (Remanent) Magnetization are Absent | p. 67 |
Equations for the scalar potential | p. 67 |
Theorem of Uniqueness and Boundary-Value Problems | p. 69 |
The first boundary-value problem | p. 70 |
The second boundary-value problem | p. 72 |
Boundary-value problem in the presence of an interface of media with different [mu] | p. 73 |
A Cylinder in a Uniform Magnetic Field | p. 75 |
Solution of the boundary problem | p. 75 |
Determination of unknown coefficients and field expressions | p. 79 |
Distribution of magnetization currents | p. 81 |
Behavior of the magnetic field inside the cylinder | p. 82 |
Induced magnetization vector | p. 82 |
Medium of small susceptibility | p. 83 |
Secondary field outside the cylinder | p. 84 |
The primary field is directed along the cylinder axis | p. 85 |
An Elongated Spheroid in a Uniform Magnetic Field B[subscript 0] | p. 86 |
Laplace's equation and its solution in spheroidal system of coordinates | p. 86 |
Field of a Magnetic Dipole Located at the Cylinder Axis | p. 92 |
Solution of Laplace's equation in the cylindrical coordinates | p. 93 |
Expressions for the potential of the magnetic fiel | p. 97 |
Coefficients A[subscript m] and B[subscript m] | p. 98 |
The current density | p. 100 |
Asymptotic behavior of the field on the cylinder (borehole) axis | p. 100 |
Concept of geometric factor | p. 102 |
Ellipsoid in a Uniform Magnetic Field | p. 104 |
System of ellipsoidal coordinates | p. 104 |
Expressions for the potential of the primary field | p. 106 |
Solutions of Laplace's equation | p. 107 |
Potential inside and outside an ellipsoid | p. 108 |
Spherical Layer in a Uniform Magnetic Field | p. 111 |
Spherical magnetic body in a uniform field | p. 114 |
Thin spherical shell in a uniform field | p. 115 |
The Magnetic Field Due to Permanent Magnet | p. 116 |
The vector potential | p. 117 |
The field outside of a thin cylinder | p. 118 |
Scalar potential | p. 122 |
The Magnet in a Uniform Magnetic Field | p. 124 |
Force acting on a free charge | p. 124 |
Linear current circuit in a uniform magnetic field B | p. 125 |
Resultant force | p. 126 |
Moment of rotation | p. 126 |
Thin and elongated magnet in a uniform magnetic field | p. 128 |
Interaction between Two Magnets | p. 130 |
Two magnets are placed along the same line (Fig 3.8) | p. 130 |
Current circuit in the magnetic field B | p. 133 |
Magnet in a field of a point magnetic charge | p. 135 |
Magnetic force | p. 135 |
Moment of rotation | p. 137 |
Energy of Magnetic Dipole in the Presence of the Magnetic Field | p. 138 |
Permanent Magnet and Measurements of the Magnetic Field | p. 139 |
Deflection method of measurements | p. 141 |
Theory of the vertical magnetometer | p. 143 |
Main Magnetic Field of the Earth | |
Elements of the Magnetic Field of the Earth | p. 147 |
History of the Earth Magnetism Study | p. 149 |
The discovery of the magnetic compass | p. 149 |
Pierre de Maricourt (Petrus Peregrinus) | p. 149 |
Magnetic compass and navigation | p. 150 |
William Gilbert (1540-1603) | p. 150 |
Edmond Halley (1656-1742) | p. 151 |
Charles Coulomb (1736-1806) | p. 152 |
Oersted (1777-1851) | p. 153 |
Andre-Marie Ampere (1777-1836) | p. 154 |
Carl Gauss (1777-1855) | p. 155 |
Solution of the Laplace Equation | p. 156 |
Orthogonality of Functions S[subscript n] | p. 158 |
Solution of Equation (4.13) for the Functions S | p. 159 |
Legendre's Equation and Zonal Harmonics | p. 160 |
Solution of Legendre's Equation | p. 161 |
Index n of functions p[subscript n] and q[subscript n] is positive | p. 162 |
Recursion Formulas for the Functions p and q | p. 163 |
Legendre Polynomials | p. 164 |
Recursion formulas for Legendre's polynomials | p. 166 |
Integral from a Product of Legendre Polynomials | p. 166 |
Expansion of Functions by Legendre Polynomials | p. 167 |
Expressions for Legendre polynomials | p. 168 |
Spherical Analysis of the Earth's Magnetic Field When the Potential is Independent of Longitude | p. 168 |
The Physical Meaning of Coefficients B[subscript n] | p. 171 |
Associated Legendre Functions | p. 172 |
Examples of the associated Legendre functions ([mu] < 1) | p. 174 |
Integrals from a product of the associated Legendre functions | p. 175 |
Spherical Harmonic Analysis of the Magnetic Field of the Earth | p. 176 |
Uniqueness and the Solution of the Forward and Inverse Problems | |
Introduction | p. 185 |
Poisson's Relationship between Potentials U and U[subscript a] | p. 188 |
Solution of the Forward Problem When the Interaction between Magnetization Currents is Negligible | p. 190 |
Development of a Solution of the Forward and Inverse Problems | p. 194 |
Example 1: Uniform half space | p. 195 |
Example 2: Layer of finite thickness | p. 196 |
Concept of Uniqueness and the Solution of the Inverse Problem in the Magnetic Method | p. 197 |
Main steps of interpretation | p. 197 |
Uniqueness and its application | p. 199 |
Solution of the Inverse Problem and Influence of Noise | p. 202 |
Paramagnetism, Diamagnetism, and Ferromagnetism | |
Introduction | p. 207 |
The Angular Momentum and Magnetic Moment of an Atom | p. 208 |
Motion of Atomic Magnetic Dipole in an External Magnetic Field | p. 212 |
The first approach | p. 212 |
Frequency of precession | p. 214 |
The second approach | p. 215 |
Magnetic Moment, Angular Momentum, Spin, and Energy States of Atomic System | p. 217 |
Magnetic moment | p. 217 |
Angular momentum | p. 218 |
Magnetic energy of atomic particle | p. 219 |
The Stern-Gerlach experiment | p. 221 |
Alternating magnetic field and transition between energy levels of atom | p. 223 |
The Rabi molecular beam method | p. 225 |
Diamagnetism | p. 228 |
Paramagnetism | p. 231 |
Classical physics approach | p. 231 |
Quantum mechanics approach | p. 235 |
Ferromagnetism | p. 237 |
Introduction | p. 237 |
The magnetization curve | p. 237 |
Hysteresis loop | p. 240 |
Principle of the Fluxgate Magnetometer | p. 241 |
Magnetization and Magnetic Forces | p. 243 |
Spontaneous magnetization | p. 247 |
Curie temperature | p. 248 |
Spontaneous magnetization and Weiss domains | p. 250 |
Case one: Single crystal of ferromagnetic and its domains | p. 251 |
Case two: Polycrystalline material of ferromagnetic | p. 252 |
Nuclear Magnetism Resonance and Measurements of Magnetic Field | |
Introduction | p. 255 |
The Vector of Nuclear Magnetization | p. 258 |
Equations of the Vector of Magnetization | p. 261 |
Case 1: Additional field is absent | p. 263 |
Case 2: The additional field is horizontal | p. 263 |
Rotating System of Coordinates | p. 264 |
Behavior of the Vector P in the Rotating System of Coordinates | p. 266 |
Example 1 | p. 266 |
Example 2: The additional field rotates in the horizontal plane | p. 267 |
The case of resonance ([omega] = [omega subscript 0] = [gamma]B[subscript 0]) | p. 267 |
General case ([omega not equal omega subscript 0]) | p. 269 |
Additional field B[subscript 1] is a sinusoidal function | p. 273 |
Magnetization Caused by the Additional Field | p. 274 |
Bloch Equations | p. 275 |
Solution of Bloch's equations when the additional field is absent | p. 276 |
Measurements of Relaxation Processes | p. 278 |
Introduction | p. 278 |
Measurements of a decay of the longitudinal component of the vector P | p. 279 |
Measurements of a decay of the transversal component of the vector P | p. 281 |
Spin echoes or refocusing | p. 282 |
Two Methods of Measuring Magnetic Field | p. 283 |
Proton precession magnetometer | p. 283 |
Optically pumped magnetometers | p. 285 |
Bibliography | p. 289 |
Appendix | p. 291 |
Subject Index | p. 297 |
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