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Electromagnetism sets a new standard in physics education. Throughout the book, the theory is illustrated with real-life applications in modern technology. It also includes detailed worked examples and step-by-step explanations to help readers develop their problem-solving strategies and skills and consolidate their understanding. In addition to a meticulous development of these traditional, analytical mathematical approaches, readers are also introduced to a range of techniques required for solving problems using computers. Electromagnetism provides an ideal preparation for students who plan more advanced studies in electrodynamics as well as those moving into industry or engineering.
| History and Perspective | p. 1 |
| Brief History of the Science of Electromagnetism | p. 1 |
| Electromagnetism in the Standard Model | p. 5 |
| Vector Calculus | p. 9 |
| Vector Algebra | p. 10 |
| Definitions | p. 10 |
| Addition and Multiplication of Vectors | p. 13 |
| Vector Product Identities | p. 14 |
| Geometric Meanings | p. 16 |
| Vector Differential Operators | p. 18 |
| Gradient of a Scalar Function | p. 18 |
| Divergence of a Vector Function | p. 19 |
| Curl of a Vector Function | p. 20 |
| Del Identities | p. 23 |
| Integral Theorems | p. 25 |
| Gauss's Theorem | p. 26 |
| Stokes's Theorem | p. 27 |
| Vector Calculus in Fluid Mechanics | p. 29 |
| Curvilinear Coordinates | p. 30 |
| General Derivations | p. 30 |
| Cartesian, Cylindrical, and Spherical Coordinates | p. 33 |
| The Helmholtz Theorem | p. 37 |
| Basic Principles of Electrostatics | p. 44 |
| Coulomb's Law | p. 44 |
| The Superposition Principle | p. 46 |
| The Electric Field | p. 46 |
| Definition | p. 46 |
| Charge as the Source of E | p. 47 |
| Field of a Charge Continuum | p. 49 |
| Curl and Divergence of E | p. 54 |
| Field Theory Versus Action at a Distance | p. 56 |
| Boundary Conditions of the Electrostatic Field | p. 56 |
| The Integral Form of Gauss's Law | p. 57 |
| Flux and Charge | p. 57 |
| Proof of Gauss's Law | p. 57 |
| Calculations Based on Gauss's Law | p. 59 |
| Green's Function and the Dirac delta Function | p. 62 |
| The Dirac delta Function | p. 62 |
| Another Proof of Gauss's Law | p. 65 |
| The Electric Potential | p. 65 |
| Definition and Construction | p. 65 |
| Poisson's Equation | p. 68 |
| Example Calculations of V (x) | p. 69 |
| Energy of the Electric Field | p. 72 |
| The Multipole Expansion | p. 75 |
| Two Charges | p. 75 |
| The Electric Dipole | p. 77 |
| Moments of a General Charge Distribution | p. 78 |
| Equipotentials and Field Lines | p. 79 |
| Torque and Potential Energy for a Dipole in an Electric Field | p. 80 |
| Applications | p. 82 |
| Chapter Summary | p. 83 |
| Electrostatics and Conductors | p. 92 |
| Electrostatic properties of conductors | p. 93 |
| Electrostatic Problems with Rectangular Symmetry | p. 98 |
| Charged Plates | p. 98 |
| Problems with Rectangular Symmetry and External Point Charges. The Method of Images | p. 102 |
| Problems with Spherical Symmetry | p. 107 |
| Charged Spheres | p. 107 |
| Problems with Spherical Symmetry and External Charges | p. 113 |
| Problems with Cylindrical Symmetry | p. 116 |
| Charged Lines and Cylinders | p. 116 |
| Problems with Cylindrical Symmetry and an External Line Charge | p. 124 |
| General Methods for Laplace's Equation | p. 133 |
| Separation of Variables for Cartesian Coordinates | p. 135 |
| Separable Solutions for Cartesian Coordinates | p. 136 |
| Examples | p. 138 |
| Separation of Variables for Spherical Polar Coordinates | p. 147 |
| Separable Solutions for Spherical Coordinates | p. 147 |
| Legendre Polynomials | p. 149 |
| Examples with Spherical Boundaries | p. 150 |
| Separation of Variables for Cylindrical Coordinates | p. 159 |
| Separable Solutions for Cylindrical Coordinates | p. 160 |
| Conjugate Functions in 2 Dimensions | p. 163 |
| Iterative Relaxation: A Numerical Method | p. 172 |
| Electrostatics and Dielectrics | p. 186 |
| The Atom as an Electric Dipole | p. 187 |
| Induced Dipoles | p. 187 |
| Polar Molecules | p. 189 |
| Polarization and Bound Charge | p. 191 |
| The Displacement Field | p. 195 |
| Linear Dielectrics | p. 197 |
| The Clausius-Mossotti Formula | p. 198 |
| Poisson's Equation in a Uniform Linear Dielectric | p. 200 |
| Dielectric Material in a Capacitor | p. 201 |
| Design of Capacitors | p. 203 |
| Microscopic Theory | p. 204 |
| Energy in a Capacitor | p. 205 |
| A Concrete Model of a Dielectric | p. 207 |
| Boundary Value Problems with Dielectric | p. 208 |
| The Boundary Conditions | p. 208 |
| A Dielectric Sphere in an Applied Field | p. 209 |
| A Point Charge above a Dielectric with a Plannar Boundary Surface | p. 211 |
| A Capacitor Partially Filled with Dielectric | p. 212 |
| Electric Currents | p. 222 |
| Electric Current in a Wire | p. 222 |
| Current Density and the Continuity Equation | p. 224 |
| Local Conservation of Charge | p. 226 |
| Boundary Condition on J(x, t) | p. 226 |
| Current and Resistance | p. 228 |
| Ohm's Law | p. 228 |
| Fabrication of Resistors | p. 233 |
| The Surface Charge on a Current Carrying Wire | p. 234 |
| A Classical Model of Conductivity | p. 236 |
| Joule's Law | p. 238 |
| Decay of a Charge Density Fluctuation | p. 239 |
| I-V Characteristic of a Vacuum-Tube Diode | p. 241 |
| Chapter Summary | p. 246 |
| Magnetostatics | p. 252 |
| The Magnetic Force and the Magnetic Field | p. 253 |
| Force on a Moving Charge | p. 253 |
| Force on a Current-Carrying Wire | p. 255 |
| Applications of the Magnetic Force | p. 255 |
| Helical or Circular Motion of q in Uniform B | p. 255 |
| Cycloidal Motion of q in Crossed E and B | p. 258 |
| Electric Motors | p. 260 |
| Electric Current as a Source of Magnetic Field | p. 262 |
| The Biot-Savart Law | p. 262 |
| Forces on Parallel Wires | p. 266 |
| General Field Equations for B(x) | p. 267 |
| Ampere's Law | p. 270 |
| Ampere Law Calculations | p. 271 |
| Formal Proof of Ampere's Law | p. 277 |
| The Vector Potential | p. 280 |
| General Solution for A(x) | p. 281 |
| The Magnetic Dipole | p. 284 |
| Asymptotic Analysis | p. 284 |
| Dipole Moment of a Planar Loop | p. 286 |
| Torque and Potential Energy of a Magnetic Dipole | p. 287 |
| The Magnetic Field of the Earth | p. 291 |
| The Full Field of a Current Loop | p. 291 |
| Magnetic Fields and Matter | p. 307 |
| The Atom as a Magnetic Dipole | p. 307 |
| Diamagnetism | p. 310 |
| Paramagnetism | p. 313 |
| Magnetization and Bound Currents | p. 314 |
| Examples | p. 316 |
| A Geometric Derivation of the Bound Currents | p. 320 |
| Ampere's Law for Free Currents, and H | p. 323 |
| The Integral Form of Ampere's Law | p. 326 |
| The Constitutive Equation | p. 326 |
| Magnetic Susceptibilities | p. 326 |
| Boundary Conditions for Magnetic Fields | p. 329 |
| Problems Involving Free Currents and Magnetic Materials | p. 331 |
| A Magnetic Body in an External Field: The Magnetic Scalar Potential [phi subscript m](x) | p. 335 |
| Ferromagnetism | p. 342 |
| Measuring Magnetization Curves: The Rowland Ring | p. 343 |
| Magnetization Curves of Ferromagnetic Materials | p. 345 |
| The Permeability of a Ferromagnetic Material | p. 346 |
| Electromagnetic Induction | p. 355 |
| Motional EMF | p. 356 |
| Electromotive Force | p. 356 |
| EMF from Motion in B | p. 357 |
| The Faraday Disk Generator | p. 358 |
| Faraday's Law of Electromagnetic Induction | p. 360 |
| Mathematical Statement | p. 361 |
| Lenz's Law | p. 363 |
| Eddy Currents | p. 364 |
| Applications of Faraday's Law | p. 368 |
| The Electric Generator and Induction Motor | p. 369 |
| The Betatron | p. 371 |
| Self-Inductance | p. 372 |
| Classical Model of Diamagnetism | p. 375 |
| Mutual Inductance | p. 376 |
| Magnetic Field Energy | p. 382 |
| Energy in a Ferromagnet | p. 386 |
| The Maxwell Equations | p. 397 |
| The Maxwell Equations in Vacuum and the Displacement Current | p. 398 |
| The Displacement Current | p. 399 |
| Scalar and Vector Potentials | p. 405 |
| Gauge Transformations and Gauge Invariance | p. 406 |
| Gauge Choices and Equations for A(x,t) and V(x,t) | p. 407 |
| The Maxwell Equations in Matter | p. 410 |
| Free and Bound Charge and Current | p. 410 |
| Boundary Conditions of Fields | p. 413 |
| Energy and Momentum of Electromagnetic Fields | p. 415 |
| Poynting's Theorem | p. 416 |
| Field Momentum | p. 421 |
| Electromagnetic Waves in Vacuum | p. 423 |
| Derivation of the Wave Equation | p. 424 |
| An Example of a Plane Wave Solution | p. 425 |
| Derivation of the General Plane Wave Solution | p. 431 |
| A Spherical Harmonic Wave | p. 434 |
| The Theory of Light | p. 437 |
| Electromagnetism and Relativity | p. 445 |
| Coordinate Transformations | p. 446 |
| The Galilean Transformation | p. 446 |
| The Lorentz Transformation | p. 448 |
| Examples Involving the Lorentz Transformation | p. 450 |
| Minkowski Space | p. 452 |
| 4-vectors, Scalars, and Tensors | p. 452 |
| Kinematics of a Point Particle | p. 455 |
| Relativistic Dynamics | p. 457 |
| Electromagnetism in Covariant Form | p. 458 |
| The Lorentz Force and the Field Tensor | p. 458 |
| Maxwell's Equations in Covariant Form | p. 460 |
| The 4-vector Potential | p. 462 |
| Field Transformations | p. 463 |
| Fields Due to a Point Charge in Uniform Motion | p. 468 |
| Magnetism from Relativity | p. 474 |
| The Energy-Momentum Flux Tensor | p. 477 |
| Electromagnetism and Optics | p. 485 |
| Electromagnetic Waves in a Dielectric | p. 485 |
| Reflection and Refraction at a Dielectric Interface | p. 488 |
| Wave Vectors | p. 490 |
| Reflectivity for Normal Incidence | p. 494 |
| Reflection for Incidence at Arbitrary Angles: Fresnel's Equations | p. 498 |
| Electromagnetic Waves in a Conductor | p. 505 |
| Reflectivity of a Good Conductor | p. 509 |
| A Classical Model of Dispersion: The Frequency Dependence of Material Properties | p. 511 |
| Dispersion in a Dielectric | p. 512 |
| Dispersion in a Plasma | p. 514 |
| Wave Guides and Transmission Lines | p. 523 |
| Electromagnetic Waves Between Parallel Conducting Planes | p. 524 |
| The TEM Solution | p. 526 |
| TE Waves | p. 528 |
| TM Waves | p. 537 |
| Summary | p. 540 |
| The Rectangular Wave Guide | p. 540 |
| Transverse Electric Modes TE(m, n) | p. 541 |
| Transverse Magnetic Modes TM(m, n) | p. 547 |
| Wave Guide of Arbitrary Shape | p. 549 |
| The TEM Mode of a Coaxial Cable | p. 551 |
| Cavity Resonance | p. 555 |
| Radiation of Electromagnetic Waves | p. 560 |
| The Retarded Potentials | p. 561 |
| Green's Functions | p. 561 |
| Radiation from an Electric Dipole | p. 567 |
| The Hertzian Dipole | p. 571 |
| Atomic Transitions | p. 574 |
| Magnetic Dipole Radiation | p. 575 |
| Complete Fields of a Hertzian Dipole | p. 577 |
| The Half-Wave Linear Antenna | p. 579 |
| The Larmor Formula: Radiation from a Point Charge | p. 584 |
| Classical Electron Theory of Light Scattering | p. 589 |
| Complete Fields of a Point Charge: The Lienard-Wiechert Potentials | p. 593 |
| A Charge with Constant Velocity | p. 596 |
| The Complete Fields | p. 598 |
| Generalization of the Larmor Formula | p. 599 |
| Electric and Magnetic Units | p. 607 |
| The Helmholtz Theorem | p. 610 |
| Index | p. 613 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
ISBN: 9780805385670
ISBN-10: 0805385673
Audience:
Professional
Format:
Hardcover
Language:
English
Number Of Pages: 680
Published: 2nd October 2001
Dimensions (cm): 23.9 x 19.1
x 3.8
Weight (kg): 1.107
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