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| 1 | History and Perspective | 1 | |||||||||
| 1.1 | Brief History of the Science of Electromagnetism | 1 | |||||||||
| 1.2 | Electromagnetism in the Standard Model | 5 | |||||||||
| 2 | Vector Calculus | 9 | |||||||||
| 2.1 | Vector Algebra | 10 | |||||||||
| 2.1.1 | Definitions | 10 | |||||||||
| 2.1.2 | Addition and Multiplication of Vectors | 13 | |||||||||
| 2.1.3 | Vector Product Identities | 14 | |||||||||
| 2.1.4 | Geometric Meanings | 16 | |||||||||
| 2.2 | Vector Differential Operators | 18 | |||||||||
| 2.2.1 | Gradient of a Scalar Function | 18 | |||||||||
| 2.2.2 | Divergence of a Vector Function | 19 | |||||||||
| 2.2.3 | Curl of a Vector Function | 20 | |||||||||
| 2.2.4 | Del Identities | 23 | |||||||||
| 2.3 | Integral Theorems | 25 | |||||||||
| 2.3.1 | Gauss's Theorem | 26 | |||||||||
| 2.3.2 | Stokes's Theorem | 27 | |||||||||
| 2.3.3 | Vector Calculus in Fluid Mechanics | 29 | |||||||||
| 2.4 | Curvilinear Coordinates | 30 | |||||||||
| 2.4.1 | General Derivations | 30 | |||||||||
| 2.4.2 | Cartesian, Cylindrical, and Spherical Coordinates | 33 | |||||||||
| 2.5 | The Helmholtz Theorem | 37 | |||||||||
| 3 | Basic Principles of Electrostatics | 44 | |||||||||
| 3.1 | Coulomb's Law | 44 | |||||||||
| 3.1.1 | The Superposition Principle | 46 | |||||||||
| 3.2 | The Electric Field | 46 | |||||||||
| 3.2.1 | Definition | 46 | |||||||||
| 3.2.2 | Charge as the Source of E | 47 | |||||||||
| 3.2.3 | Field of a Charge Continuum | 49 | |||||||||
| 3.3 | Curl and Divergence of E | 54 | |||||||||
| 3.3.1 | Field Theory Versus Action at a Distance | 56 | |||||||||
| 3.3.2 | Boundary Conditions of the Electrostatic Field | 56 | |||||||||
| 3.4 | The Integral Form of Gauss's Law | 57 | |||||||||
| 3.4.1 | Flux and Charge | 57 | |||||||||
| 3.4.2 | Proof of Gauss's Law | 57 | |||||||||
| 3.4.3 | Calculations Based on Gauss's Law | 59 | |||||||||
| 3.5 | Green's Function and the Dirac delta Function | 62 | |||||||||
| 3.5.1 | The Dirac delta Function | 62 | |||||||||
| 3.5.2 | Another Proof of Gauss's Law | 65 | |||||||||
| 3.6 | The Electric Potential | 65 | |||||||||
| 3.6.1 | Definition and Construction | 65 | |||||||||
| 3.6.2 | Poisson's Equation | 68 | |||||||||
| 3.6.3 | Example Calculations of V (x) | 69 | |||||||||
| 3.7 | Energy of the Electric Field | 72 | |||||||||
| 3.8 | The Multipole Expansion | 75 | |||||||||
| 3.8.1 | Two Charges | 75 | |||||||||
| 3.8.2 | The Electric Dipole | 77 | |||||||||
| 3.8.3 | Moments of a General Charge Distribution | 78 | |||||||||
| 3.8.4 | Equipotentials and Field Lines | 79 | |||||||||
| 3.8.5 | Torque and Potential Energy for a Dipole in an Electric Field | 80 | |||||||||
| 3.9 | Applications | 82 | |||||||||
| 3.10 | Chapter Summary | 83 | |||||||||
| 4 | Electrostatics and Conductors | 92 | |||||||||
| 4.1 | Electrostatic properties of conductors | 93 | |||||||||
| 4.2 | Electrostatic Problems with Rectangular Symmetry | 98 | |||||||||
| 4.2.1 | Charged Plates | 98 | |||||||||
| 4.2.2 | Problems with Rectangular Symmetry and External Point Charges. The Method of Images | 102 | |||||||||
| 4.3 | Problems with Spherical Symmetry | 107 | |||||||||
| 4.3.1 | Charged Spheres | 107 | |||||||||
| 4.3.2 | Problems with Spherical Symmetry and External Charges | 113 | |||||||||
| 4.4 | Problems with Cylindrical Symmetry | 116 | |||||||||
| 4.4.1 | Charged Lines and Cylinders | 116 | |||||||||
| 4.4.2 | Problems with Cylindrical Symmetry and an External Line Charge | 124 | |||||||||
| 5 | General Methods for Laplace's Equation | 133 | |||||||||
| 5.1 | Separation of Variables for Cartesian Coordinates | 135 | |||||||||
| 5.1.1 | Separable Solutions for Cartesian Coordinates | 136 | |||||||||
| 5.1.2 | Examples | 138 | |||||||||
| 5.2 | Separation of Variables for Spherical Polar Coordinates | 147 | |||||||||
| 5.2.1 | Separable Solutions for Spherical Coordinates | 147 | |||||||||
| 5.2.2 | Legendre Polynomials | 149 | |||||||||
| 5.2.3 | Examples with Spherical Boundaries | 150 | |||||||||
| 5.3 | Separation of Variables for Cylindrical Coordinates | 159 | |||||||||
| 5.3.1 | Separable Solutions for Cylindrical Coordinates | 160 | |||||||||
| 5.4 | Conjugate Functions in 2 Dimensions | 163 | |||||||||
| 5.5 | Iterative Relaxation: A Numerical Method | 172 | |||||||||
| 6 | Electrostatics and Dielectrics | 186 | |||||||||
| 6.1 | The Atom as an Electric Dipole | 187 | |||||||||
| 6.1.1 | Induced Dipoles | 187 | |||||||||
| 6.1.2 | Polar Molecules | 189 | |||||||||
| 6.2 | Polarization and Bound Charge | 191 | |||||||||
| 6.3 | The Displacement Field | 195 | |||||||||
| 6.3.1 | Linear Dielectrics | 197 | |||||||||
| 6.3.2 | The Clausius-Mossotti Formula | 198 | |||||||||
| 6.3.3 | Poisson's Equation in a Uniform Linear Dielectric | 200 | |||||||||
| 6.4 | Dielectric Material in a Capacitor | 201 | |||||||||
| 6.4.1 | Design of Capacitors | 203 | |||||||||
| 6.4.2 | Microscopic Theory | 204 | |||||||||
| 6.4.3 | Energy in a Capacitor | 205 | |||||||||
| 6.4.4 | A Concrete Model of a Dielectric | 207 | |||||||||
| 6.5 | Boundary Value Problems with Dielectric | 208 | |||||||||
| 6.5.1 | The Boundary Conditions | 208 | |||||||||
| 6.5.2 | A Dielectric Sphere in an Applied Field | 209 | |||||||||
| 6.5.3 | A Point Charge above a Dielectric with a Plannar Boundary Surface | 211 | |||||||||
| 6.5.4 | A Capacitor Partially Filled with Dielectric | 212 | |||||||||
| 7 | Electric Currents | 222 | |||||||||
| 7.1 | Electric Current in a Wire | 222 | |||||||||
| 7.2 | Current Density and the Continuity Equation | 224 | |||||||||
| 7.2.1 | Local Conservation of Charge | 226 | |||||||||
| 7.2.2 | Boundary Condition on J(x, t) | 226 | |||||||||
| 7.3 | Current and Resistance | 228 | |||||||||
| 7.3.1 | Ohm's Law | 228 | |||||||||
| 7.3.2 | Fabrication of Resistors | 233 | |||||||||
| 7.3.3 | The Surface Charge on a Current Carrying Wire | 234 | |||||||||
| 7.4 | A Classical Model of Conductivity | 236 | |||||||||
| 7.5 | Joule's Law | 238 | |||||||||
| 7.6 | Decay of a Charge Density Fluctuation | 239 | |||||||||
| 7.7 | I-V Characteristic of a Vacuum-Tube Diode | 241 | |||||||||
| 7.8 | Chapter Summary | 246 | |||||||||
| 8 | Magnetostatics | 252 | |||||||||
| 8.1 | The Magnetic Force and the Magnetic Field | 253 | |||||||||
| 8.1.1 | Force on a Moving Charge | 253 | |||||||||
| 8.1.2 | Force on a Current-Carrying Wire | 255 | |||||||||
| 8.2 | Applications of the Magnetic Force | 255 | |||||||||
| 8.2.1 | Helical or Circular Motion of q in Uniform B | 255 | |||||||||
| 8.2.2 | Cycloidal Motion of q in Crossed E and B | 258 | |||||||||
| 8.2.3 | Electric Motors | 260 | |||||||||
| 8.3 | Electric Current as a Source of Magnetic Field | 262 | |||||||||
| 8.3.1 | The Biot-Savart Law | 262 | |||||||||
| 8.3.2 | Forces on Parallel Wires | 266 | |||||||||
| 8.3.3 | General Field Equations for B(x) | 267 | |||||||||
| 8.4 | Ampere's Law | 270 | |||||||||
| 8.4.1 | Ampere Law Calculations | 271 | |||||||||
| 8.4.2 | Formal Proof of Ampere's Law | 277 | |||||||||
| 8.5 | The Vector Potential | 280 | |||||||||
| 8.5.1 | General Solution for A(x) | 281 | |||||||||
| 8.6 | The Magnetic Dipole | 284 | |||||||||
| 8.6.1 | Asymptotic Analysis | 284 | |||||||||
| 8.6.2 | Dipole Moment of a Planar Loop | 286 | |||||||||
| 8.6.3 | Torque and Potential Energy of a Magnetic Dipole | 287 | |||||||||
| 8.6.4 | The Magnetic Field of the Earth | 291 | |||||||||
| 8.7 | The Full Field of a Current Loop | 291 | |||||||||
| 9 | Magnetic Fields and Matter | 307 | |||||||||
| 9.1 | The Atom as a Magnetic Dipole | 307 | |||||||||
| 9.1.1 | Diamagnetism | 310 | |||||||||
| 9.1.2 | Paramagnetism | 313 | |||||||||
| 9.2 | Magnetization and Bound Currents | 314 | |||||||||
| 9.2.1 | Examples | 316 | |||||||||
| 9.2.2 | A Geometric Derivation of the Bound Currents | 320 | |||||||||
| 9.3 | Ampere's Law for Free Currents, and H | 323 | |||||||||
| 9.3.1 | The Integral Form of Ampere's Law | 326 | |||||||||
| 9.3.2 | The Constitutive Equation | 326 | |||||||||
| 9.3.3 | Magnetic Susceptibilities | 326 | |||||||||
| 9.3.4 | Boundary Conditions for Magnetic Fields | 329 | |||||||||
| 9.4 | Problems Involving Free Currents and Magnetic Materials | 331 | |||||||||
| 9.5 | A Magnetic Body in an External Field: The Magnetic Scalar Potential [phi subscript m](x) | 335 | |||||||||
| 9.6 | Ferromagnetism | 342 | |||||||||
| 9.6.1 | Measuring Magnetization Curves: The Rowland Ring | 343 | |||||||||
| 9.6.2 | Magnetization Curves of Ferromagnetic Materials | 345 | |||||||||
| 9.6.3 | The Permeability of a Ferromagnetic Material | 346 | |||||||||
| 10 | Electromagnetic Induction | 355 | |||||||||
| 10.1 | Motional EMF | 356 | |||||||||
| 10.1.1 | Electromotive Force | 356 | |||||||||
| 10.1.2 | EMF from Motion in B | 357 | |||||||||
| 10.1.3 | The Faraday Disk Generator | 358 | |||||||||
| 10.2 | Faraday's Law of Electromagnetic Induction | 360 | |||||||||
| 10.2.1 | Mathematical Statement | 361 | |||||||||
| 10.2.2 | Lenz's Law | 363 | |||||||||
| 10.2.3 | Eddy Currents | 364 | |||||||||
| 10.3 | Applications of Faraday's Law | 368 | |||||||||
| 10.3.1 | The Electric Generator and Induction Motor | 369 | |||||||||
| 10.3.2 | The Betatron | 371 | |||||||||
| 10.3.3 | Self-Inductance | 372 | |||||||||
| 10.3.4 | Classical Model of Diamagnetism | 375 | |||||||||
| 10.4 | Mutual Inductance | 376 | |||||||||
| 10.5 | Magnetic Field Energy | 382 | |||||||||
| 10.5.1 | Energy in a Ferromagnet | 386 | |||||||||
| 11 | The Maxwell Equations | 397 | |||||||||
| 11.1 | The Maxwell Equations in Vacuum and the Displacement Current | 398 | |||||||||
| 11.1.1 | The Displacement Current | 399 | |||||||||
| 11.2 | Scalar and Vector Potentials | 405 | |||||||||
| 11.2.1 | Gauge Transformations and Gauge Invariance | 406 | |||||||||
| 11.2.2 | Gauge Choices and Equations for A(x,t) and V(x,t) | 407 | |||||||||
| 11.3 | The Maxwell Equations in Matter | 410 | |||||||||
| 11.3.1 | Free and Bound Charge and Current | 410 | |||||||||
| 11.3.2 | Boundary Conditions of Fields | 413 | |||||||||
| 11.4 | Energy and Momentum of Electromagnetic Fields | 415 | |||||||||
| 11.4.1 | Poynting's Theorem | 416 | |||||||||
| 11.4.2 | Field Momentum | 421 | |||||||||
| 11.5 | Electromagnetic Waves in Vacuum | 423 | |||||||||
| 11.5.1 | Derivation of the Wave Equation | 424 | |||||||||
| 11.5.2 | An Example of a Plane Wave Solution | 425 | |||||||||
| 11.5.3 | Derivation of the General Plane Wave Solution | 431 | |||||||||
| 11.5.4 | A Spherical Harmonic Wave | 434 | |||||||||
| 11.5.5 | The Theory of Light | 437 | |||||||||
| 12 | Electromagnetism and Relativity | 445 | |||||||||
| 12.1 | Coordinate Transformations | 446 | |||||||||
| 12.1.1 | The Galilean Transformation | 446 | |||||||||
| 12.1.2 | The Lorentz Transformation | 448 | |||||||||
| 12.1.3 | Examples Involving the Lorentz Transformation | 450 | |||||||||
| 12.2 | Minkowski Space | 452 | |||||||||
| 12.2.1 | 4-vectors, Scalars, and Tensors | 452 | |||||||||
| 12.2.2 | Kinematics of a Point Particle | 455 | |||||||||
| 12.2.3 | Relativistic Dynamics | 457 | |||||||||
| 12.3 | Electromagnetism in Covariant Form | 458 | |||||||||
| 12.3.1 | The Lorentz Force and the Field Tensor | 458 | |||||||||
| 12.3.2 | Maxwell's Equations in Covariant Form | 460 | |||||||||
| 12.3.3 | The 4-vector Potential | 462 | |||||||||
| 12.4 | Field Transformations | 463 | |||||||||
| 12.5 | Fields Due to a Point Charge in Uniform Motion | 468 | |||||||||
| 12.6 | Magnetism from Relativity | 474 | |||||||||
| 12.7 | The Energy-Momentum Flux Tensor | 477 | |||||||||
| 13 | Electromagnetism and Optics | 485 | |||||||||
| 13.1 | Electromagnetic Waves in a Dielectric | 485 | |||||||||
| 13.2 | Reflection and Refraction at a Dielectric Interface | 488 | |||||||||
| 13.2.1 | Wave Vectors | 490 | |||||||||
| 13.2.2 | Reflectivity for Normal Incidence | 494 | |||||||||
| 13.2.3 | Reflection for Incidence at Arbitrary Angles: Fresnel's Equations | 498 | |||||||||
| 13.3 | Electromagnetic Waves in a Conductor | 505 | |||||||||
| 13.3.1 | Reflectivity of a Good Conductor | 509 | |||||||||
| 13.4 | A Classical Model of Dispersion: The Frequency Dependence of Material Properties | 511 | |||||||||
| 13.4.1 | Dispersion in a Dielectric | 512 | |||||||||
| 13.4.2 | Dispersion in a Plasma | 514 | |||||||||
| 14 | Wave Guides and Transmission Lines | 523 | |||||||||
| 14.1 | Electromagnetic Waves Between Parallel Conducting Planes | 524 | |||||||||
| 14.1.1 | The TEM Solution | 526 | |||||||||
| 14.1.2 | TE Waves | 528 | |||||||||
| 14.1.3 | TM Waves | 537 | |||||||||
| 14.1.4 | Summary | 540 | |||||||||
| 14.2 | The Rectangular Wave Guide | 540 | |||||||||
| 14.2.1 | Transverse Electric Modes TE(m, n) | 541 | |||||||||
| 14.2.2 | Transverse Magnetic Modes TM(m, n) | 547 | |||||||||
| 14.3 | Wave Guide of Arbitrary Shape | 549 | |||||||||
| 14.4 | The TEM Mode of a Coaxial Cable | 551 | |||||||||
| 14.5 | Cavity Resonance | 555 | |||||||||
| 15 | Radiation of Electromagnetic Waves | 560 | |||||||||
| 15.1 | The Retarded Potentials | 561 | |||||||||
| 15.1.1 | Green's Functions | 561 | |||||||||
| 15.2 | Radiation from an Electric Dipole | 567 | |||||||||
| 15.2.1 | The Hertzian Dipole | 571 | |||||||||
| 15.2.2 | Atomic Transitions | 574 | |||||||||
| 15.2.3 | Magnetic Dipole Radiation | 575 | |||||||||
| 15.2.4 | Complete Fields of a Hertzian Dipole | 577 | |||||||||
| 15.3 | The Half-Wave Linear Antenna | 579 | |||||||||
| 15.4 | The Larmor Formula: Radiation from a Point Charge | 584 | |||||||||
| 15.5 | Classical Electron Theory of Light Scattering | 589 | |||||||||
| 15.6 | Complete Fields of a Point Charge: The Lienard-Wiechert Potentials | 593 | |||||||||
| 15.6.1 | A Charge with Constant Velocity | 596 | |||||||||
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Title: Electromagnetism Manufacturer: Addison-WesleyAddison-Wesley Item Number: 9780805385670 Publication Date: October 2001 Number: 1 Product Description: Electromagnetism Universal Product Code (UPC): 9780805385670 WonderClub Stock Keeping Unit (WSKU): 9780805385670 Rating: 4.5/5 based on 2 Reviews Image Location: https://wonderclub.com/images/covers/56/70/9780805385670.jpg Weight: 0.200 kg (0.44 lbs) Width: 7.500 cm (2.95 inches) Heigh : 9.100 cm (3.58 inches) Depth: 1.400 cm (0.55 inches) Date Added: August 25, 2020, Added By: Ross Date Last Edited: August 25, 2020, Edited By: Ross
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