ELECTROMAGNETISM. Second Edition. I. S. Grant W. R. Phillips. John Wiley & Sons. Department of Physics University of Manchester

Transcription

1 ELECTROMAGNETISM Second Edition I. S. Grant W. R. Phillips Department of Physics University of Manchester John Wiley & Sons CHICHESTER NEW YORK BRISBANE TORONTO SINGAPORE

2 Flow diagram inside front cover 1 FORCE AND ENERGY IN ELECTROSTATICS 1.1 Electric Charge The Electric Field Electric Fields in Matter The Atomic Charge Density The Atomic Electric Field The Macroscopic Electric Field Gauss' Law The Flux of a Vector Field The Flux of the Electric Field out of a Closed Surface The Divergence of a Vector Field The Differential Form of Gauss' Law Electrostatic Energy The Electrostatic Potential The Electric Field as the Gradient of the Potential The Dipole Potential Energy Changes Associated with the Atomic Field Capacitors, and Energy in Macroscopic Fields.. 40 * Energy Stored by a Number of Charged Conductors 44 PROBLEMS 1 46 * Starred sections may be omitted as they are not required later in the book.

3 xii 2 DIELECTRICS Polarization Relative Permittivity and Electric Susceptibility The Local Field Polar Molecules Non-polar Liquids Macroscopic Fields in Dielectrics The Volume Density of Polarization Charge The Electric Displacement Vector Boundary Conditions for D and E. Energy in the Presence of Dielectrics Some Further Remarks about Energy and Forces PROBLEMS 2 3 ELECTROSTATIC FIELD CALCULATIONS 3.1 Poisson's Equation and Laplace's Equation The Uniqueness Theorem Electric Fields in the Presence of Free Charge 3.2 Boundaries Between Different Regions.... * 3.3 Boundary Conditions and Field P a t t e r n s.... * Electrostatic Images * Spheres and Spherical Cavities in Uniform External Field * 3.4 Electrostatic Lenses * 3.5 Numerical Solutions of Poisson's Equation 3.6 Summary of Electrostatics PROBLEMS 3 4 STEADY CURRENTS AND MAGNETIC FIELDS Electromotive Force and Conduction Current and Resistance The Calculation of Resistance The Magnetic Field The Lorentz Force Magnetic Field Lines The Magnetic Dipole Current Loops in External Fields Magnetic Dipoles and Magnetic Fields Ampere's Law The Field of a Large Current Loop The Biot-Savart Law...

4 xiii Examples of the Calculation of Magnetic Fields The Differential Form of Ampere's Law The Operator Curl. * The Vector Curl В The Magnetic Vector Potential Forces and Torques on Coils Magnetic Flux 151 The Motion of Charged Particles in Electric and Magnetic Fields The Motion of a Charged Particle in a Uniform Magnetic Field Magnetic Mirrors and Plasmas Magnetic Quadrupole Lenses 159 PROBLEMS MAGNETIC MATERIALS 5.1 Magnetization Diamagnetism Paramagnetism Ferromagnetism 5.2 The Macroscopic Magnetic Field Inside Media The Surface Currents on a Uniformly Magnetized Body The Distributed Currents Within a Magnetized Body Magnetic Susceptibility and Atomic Structure 5.3 The Field Vector H Ampere's Law for the Field H The Boundary Conditions on the Field В and H. 5.4 Magnets Electromagnets * Permanent Magnets 5.5 Summary of Magnetostatics PROBLEMS ELECTROMAGNETIC INDUCTION AND MAGNETIC ENERGY 6.1 Electromagnetic Induction Motional Electromotive Force Faraday's Law Examples of Induction The Differential Form of Faraday's Law 6.2 Self-inductance and Mutual Inductance Self-inductance

5 xiv Mutual Inductance Energy and Forces in Magnetic Fields The Magnetic Energy Stored in an Inductor The Total Magnetic Energy of a System of Currents The Potential Energy of a Coil in a Field and the Force on the Coil The Total Magnetic Energy in Terms of the Fields В andh Non-linear Media 241 * Further Comments on Energy in Magnetic Fields The Measurement of Magnetic Fields and Susceptibilities The Measurement of Magnetic Fields The Measurement of Magnetic Susceptibilities. 248 PROBLEMS ALTERNATING CURRENTS AND TRANSIENTS 7.1 Alternating Current Generators Amplitude, Phase and Period Resistance, Capacitance and Inductance in A.C. Circuits The Phasor Diagram and Complex Impedance Power in A.C. Circuits Resonance Transients 274 PROBLEMS LINEAR CIRCUITS 8.1 Networks Kirchhoffs Rules Loop Analysis, Node Analysis and Superposition A.C.Networks Audio-frequency Bridges Impedance and Admittance Input Impedance Output Impedance and Thevenin's Theorem Filters Ladder Networks Higher Order Filters and Delay Lines Transformers The Ideal Transformer Applications of Transformers 311 * Real Transformers PROBLEMS 8 318

6 9 TRANSMISSION LINES Propagation of Signals in a Lossless Transmission Line Practical Types of Transmission Line The Parallel Wire Transmission Line The Coaxial Cable Parallel Strip Lines Reflections. The Input Impedance of a Mismatched Line Lossy Lines PROBLEMS 9 10 MAXWELL'S EQUATIONS 10.1 The Equation of Continuity Displacement Current Maxwell's Equations 10.4 Electromagnetic Radiation * 10.5 The Microscopic Field Equations PROBLEMS ELECTROMAGNETIC WAVES Electromagnetic Waves in Free Space Plane Waves and Polarization Plane Waves in Free Space Plane Waves in Isotropic Insulating Media Dispersion Energy in Electromagnetic Waves.... The Absorption of Plane Waves in Conductors and the Skin Effect The Reflection and Transmission of Electromagnetic Waves Boundary Conditions on Electric and Magnetic Fields Reflection at Dielectric Boundaries Reflection at Metallic Boundaries Polarization by Reflection. Electromagnetic Waves and Photons PROBLEMS WAVEGUIDES 12.1 The Propagation of Waves Between Conducting Plates Rectangular Waveguides The TE 01 Mode

7 xvi * Further Comments on Waveguides Cavities 426 PROBLEMS THE GENERATION OF ELECTROMAGNETIC WAVES 13.1 The Retarded Potentials The Hertzian Dipole Antennas 443 PROBLEMS ELECTROMAGNETISM AND SPECIAL RELATIVITY 14.1 Introductory Remarks The Lorentz Transformation Charges and Fields as seen by Different Observers Four-vectors Maxwell's Equations in Four-vector Form Transformation of the Fields Magnetism as a Relativistic Phenomenon Retarded Potentials From the Relativistic Standpoint PROBLEMS APPENDIX A UNITS A.l Electrical Units and Standards A. 1.1 The Definition of the Ampere A. 1.2 Calibration and Comparison of Electrical. Standards A.2 Gaussian Units 482 A.3 Conversion between SI and Gaussian Units APPENDIX В FIELDS AND DIFFERENTIAL OPERATORS B.l The Operators div, grad and curl B.2 Formulae in Different Coordinate Systems. 489 B.3 Identities 493 APPENDIX С THE DERIVATION OF THE BIOT-SAVART LAW Solutions to Problems 497 Further Reading 518 Index 519 Physical constants inside back cover