ELECTROMAGNETISM Second Edition I. S. Grant W. R. Phillips Department of Physics University of Manchester John Wiley & Sons CHICHESTER NEW YORK BRISBANE TORONTO SINGAPORE
Flow diagram inside front cover 1 FORCE AND ENERGY IN ELECTROSTATICS 1.1 Electric Charge 2 1.2 The Electric Field 6 1.3 Electric Fields in Matter 10 1.3.1 The Atomic Charge Density 10 1.3.2 The Atomic Electric Field 11 1.3.3 The Macroscopic Electric Field 13 1.4 Gauss' Law 16 1.4.1 The Flux of a Vector Field 17 1.4.2 The Flux of the Electric Field out of a Closed Surface 19 1.4.3 The Divergence of a Vector Field 24 1.4.4 The Differential Form of Gauss' Law.... 26 1.5 Electrostatic Energy 28 1.5.1 The Electrostatic Potential 28 1.5.2 The Electric Field as the Gradient of the Potential. 31 1.5.3 The Dipole Potential 35 1.5.4 Energy Changes Associated with the Atomic Field. 38 1.5.5 Capacitors, and Energy in Macroscopic Fields.. 40 * 1.5.6 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.
xii 2 DIELECTRICS 2.1 2.2 2.3 2.4 Polarization Relative Permittivity and Electric Susceptibility 2.2.1 The Local Field 2.2.2 Polar Molecules 2.2.3 Non-polar Liquids Macroscopic Fields in Dielectrics 2.3.1 The Volume Density of Polarization Charge 2.3.2 The Electric Displacement Vector. 2.3.3 Boundary Conditions for D and E. Energy in the Presence of Dielectrics 2.4.1 Some Further Remarks about Energy and Forces PROBLEMS 2 3 ELECTROSTATIC FIELD CALCULATIONS 3.1 Poisson's Equation and Laplace's Equation 3.1.1 The Uniqueness Theorem 3.1.2 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.... * 3.3.1 Electrostatic Images * 3.3.2 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 4.1 4.2 4.3 4.4 Electromotive Force and Conduction 4.1.1 Current and Resistance. 4.1.2 The Calculation of Resistance The Magnetic Field 4.2.1 The Lorentz Force. 4.2.2 Magnetic Field Lines The Magnetic Dipole.... 4.3.1 Current Loops in External Fields. 4.3.2 Magnetic Dipoles and Magnetic Fields Ampere's Law 4.4.1 The Field of a Large Current Loop 4.4.2 The Biot-Savart Law...
xiii 4.5 4.6 4.7 4.4.3 Examples of the Calculation of Magnetic Fields The Differential Form of Ampere's Law. 4.5.1 The Operator Curl. * 4.5.2 The Vector Curl В 4.5.3 The Magnetic Vector Potential 139 144 144 148 148 Forces and Torques on Coils 150 4.6.1 Magnetic Flux 151 The Motion of Charged Particles in Electric and Magnetic Fields 154 4.7.1 The Motion of a Charged Particle in a Uniform Magnetic Field 155 4.7.2 Magnetic Mirrors and Plasmas 157 4.7.3 Magnetic Quadrupole Lenses 159 PROBLEMS 4 163 5 MAGNETIC MATERIALS 5.1 Magnetization. 5.1.1 Diamagnetism 5.1.2 Paramagnetism 5.1.3 Ferromagnetism 5.2 The Macroscopic Magnetic Field Inside Media 5.2.1 The Surface Currents on a Uniformly Magnetized Body 5.2.2 The Distributed Currents Within a Magnetized Body 5.2.3 Magnetic Susceptibility and Atomic Structure 5.3 The Field Vector H 5.3.1 Ampere's Law for the Field H 5.3.2 The Boundary Conditions on the Field В and H. 5.4 Magnets.... 5.4.1 Electromagnets * 5.4.2 Permanent Magnets 5.5 Summary of Magnetostatics PROBLEMS 5... 166 169 173 175 176 178 179 183 186 186 191 194 194 204 208 209 6 ELECTROMAGNETIC INDUCTION AND MAGNETIC ENERGY 6.1 Electromagnetic Induction.... 6.1.1 Motional Electromotive Force 6.1.2 Faraday's Law 6.1.3 Examples of Induction.... 6.1.4 The Differential Form of Faraday's Law 6.2 Self-inductance and Mutual Inductance. 6.2.1 Self-inductance 212 214 218 221 228 230 230
xiv 6.2.2 Mutual Inductance 232 6.3 Energy and Forces in Magnetic Fields 234 6.3.1 The Magnetic Energy Stored in an Inductor... 234 6.3.2 The Total Magnetic Energy of a System of Currents. 235 6.3.3 The Potential Energy of a Coil in a Field and the Force on the Coil 237 6.3.4 The Total Magnetic Energy in Terms of the Fields В andh 239 6.3.5 Non-linear Media 241 * 6.3.6 Further Comments on Energy in Magnetic Fields.. 243 6.4 The Measurement of Magnetic Fields and Susceptibilities. 246 6.4.1 The Measurement of Magnetic Fields.... 246 6.4.2 The Measurement of Magnetic Susceptibilities. 248 PROBLEMS 6 250 7 ALTERNATING CURRENTS AND TRANSIENTS 7.1 Alternating Current Generators....... 253 7.2 Amplitude, Phase and Period 256 7.3 Resistance, Capacitance and Inductance in A.C. Circuits.. 257 7.4 The Phasor Diagram and Complex Impedance. 260 7.5 Power in A.C. Circuits 266 7.6 Resonance... 268 7.7 Transients 274 PROBLEMS 7 280 8 LINEAR CIRCUITS 8.1 Networks 282 8.1.1 Kirchhoffs Rules 283 8.1.2 Loop Analysis, Node Analysis and Superposition.. 286 8.1.3 A.C.Networks 288 8.2 Audio-frequency Bridges 291 8.3 Impedance and Admittance 293 8.3.1 Input Impedance 296 8.3.2 Output Impedance and Thevenin's Theorem... 297 8.4 Filters 299 8.4.1 Ladder Networks 301 8.4.2 Higher Order Filters and Delay Lines.... 303 8.5 Transformers 307 8.5.1 The Ideal Transformer 308 8.5.2 Applications of Transformers 311 * 8.5.3 Real Transformers.. 312 PROBLEMS 8 318
9 TRANSMISSION LINES 9.1 9.2 9.3 9.4 9.5 Propagation of Signals in a Lossless Transmission Line Practical Types of Transmission Line 9.2.1 The Parallel Wire Transmission Line 9.2.2 The Coaxial Cable. 9.2.3 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. 10.2 Displacement Current. 10.3 Maxwell's Equations 10.4 Electromagnetic Radiation * 10.5 The Microscopic Field Equations PROBLEMS 10. 11 ELECTROMAGNETIC WAVES 11.1 11.2 11.3 11.4 11.5 11.6 11.7 Electromagnetic Waves in Free Space Plane Waves and Polarization.... 11.2.1 Plane Waves in Free Space 11.2.2 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 11.6.1 Boundary Conditions on Electric and Magnetic Fields 11.6.2 Reflection at Dielectric Boundaries 11.6.3 Reflection at Metallic Boundaries 11.6.4 Polarization by Reflection. Electromagnetic Waves and Photons PROBLEMS 11 12 WAVEGUIDES 12.1 The Propagation of Waves Between Conducting Plates. 12.2 Rectangular Waveguides 12.2.1 The TE 01 Mode 409 415 420
xvi * 12.2.2 Further Comments on Waveguides.... 423 12.3 Cavities 426 PROBLEMS 12 430 13 THE GENERATION OF ELECTROMAGNETIC WAVES 13.1 The Retarded Potentials 433 13.2 The Hertzian Dipole 436 13.3 Antennas 443 PROBLEMS 13 450 14 ELECTROMAGNETISM AND SPECIAL RELATIVITY 14.1 Introductory Remarks 451 14.2 The Lorentz Transformation 452 14.3 Charges and Fields as seen by Different Observers... 455 14.4 Four-vectors 458 14.5 Maxwell's Equations in Four-vector Form.... 461 14.6 Transformation of the Fields....... 464 14.7 Magnetism as a Relativistic Phenomenon.... 469 14.8 Retarded Potentials From the Relativistic Standpoint.. 473 PROBLEMS 14 476 APPENDIX A UNITS A.l Electrical Units and Standards.... 477 A. 1.1 The Definition of the Ampere.. 477 A. 1.2 Calibration and Comparison of Electrical. Standards.. 479 A.2 Gaussian Units 482 A.3 Conversion between SI and Gaussian Units.. 485 APPENDIX В FIELDS AND DIFFERENTIAL OPERATORS B.l The Operators div, grad and curl.... 487 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