Electromagnetism

I. S. Grant and W. R. Phillips are the authors of Electromagnetism, 2nd Edition, published by Wiley.

• 1 Force and Energy in Electrostatics1.1 Electric Charge 21.2 The Electric Field 61.3 Electric Fields in Matter 101.3.1 The Atomic Charge Density 101.3.2 The Atomic Electric Field 111.3.3 The Macroscopic Electric Field 131.4 Gauss' Law 161.4.1 The Flux of a Vector Field 171.4.2 The Flux of the Electric Field out of a Closed Surface 191.4.3 The Divergence of a Vector Field 241.4.4 The Differential Form of Gauss' Law 261.5 Electrostatic Energy 281.5.1 The Electrostatic Potential 281.5.2 The Electric Field as the Gradient of the Potential 311.5.3 The Dipole Potential 351.5.4 Energy Changes Associated with the Atomic Field 381.5.5 Capacitors, and Energy in Macroscopic Fields 40* 1.5.6 Energy Stored by a Number of Charged Conductors 44Problems 1 462 Dielectrics2.1 Polarization 492.2 Relative Permittivity and Electric Susceptibility 552.2.1 The Local Field 592.2.2 Polar Molecules 602.2.3 Non-polar Liquids. 672.3 Macroscopic Fields in Dielectrics 702.3.1 The Volume Density of Polarization Charge. 712.3.2 The Electric Displacement Vector 732.3.3 Boundary Conditions for D and E. 762.4 Energy in the Presence of Dielectrics 79* 2.4.1 Some Further Remarks about Energy and Forces. 80Problems 2 823 Electrostatic Field Calculations3.1 Poisson's Equation and Laplace's Equation 853.1.1 The Uniqueness Theorem 883.1.2 Electric Fields ·in the Presence of Free Charge 893.2 Boundaries Between Different Regions 91* 3.3 Boundary Conditions and Field Patterns 93* 3.3.1 Electrostatic Images 93* 3.3.2 Spheres and Spherical Cavities in Uniform External Field 973.4 Electrostatic Lenses 100* 3.5 Numerical Solutions of Poisson's Equation 1033.6 Summary of Electrostatics 107Problems 3 1094 Steady Currents and Magnetic Fields4.1 Electromotive Force and Conduction 1124.1.1 Current and Resistance 112* 4.1.2 The Calculation of Resistance 1164.2 The Magnetic Field 1194.2.1 The Lorentz Force 1194.2.2 Magnetic Field Lines 1234.3 The Magnetic Dipole 1274.3.1 Current Loops in External Fields 1274.3.2 Magnetic Dipoles and Magnetic Fields 1304.4 Ampere's Law 1324.4.1 The Field of a Large Current Loop 1324.4.2 The Biot−Savart Law 1374.4.3 Examples of the Calculation of Magnetic Fields 1394.5 The Differential Form of Ampere's Law 1444.5.1 The Operator Curl. 1444.5.2 The Vector Curl B 1484.5.3 The Magnetic Vector Potential 1484.6 Forces and Torques on Coils 1504.6.1 Magnetic Flux 1514.7 The Motion of Charged Particles in Electric and Magnetic Fields 1544.7.1 The Motion of a Charged Particle in a Uniform Magnetic Field 1554.7.2 Magnetic Mirrors and Plasmas 157* 4.7.3 Magnetic Quadrupole Lenses 159Problems 4 1635 Magnetic Materials5.1 Magnetization 1665.1.1 Diamagnetism 1695.1.2 Paramagnetism 1735.1.3 Ferromagnetism 1755.2 The Macroscopic Magnetic Field Inside Media 1765.2.1 The Surface Currents on a Uniformly Magnetized Body 1785.2.2 The Distributed Currents Within a Magnetized Body 1795.2.3 Magnetic Susceptibility and Atomic Structure 1835.3 The Field Vector H 1865.3.1 Ampere's Law for the Field H 1865.3.2 The Boundary Conditions on the Field Band H 1915.4 Magnets 1945.4.1 Electromagnets 194* 5.4.2 Permanent Magnets 2045.5 Summary of Magnetostatics 208Problems 5 2096 Electromagnetic Induction and Magnetic Energy6.1 Electromagnetic Induction 2126.1.1 Motional Electromotive Force 2146.1.2 Faraday's Law 2186.1.3 Examples of Induction 2216.1.4 The Differential Form of Faraday's Law 2286.2 Self-inductance and Mutual Inductance 2306.2.1 Self-inductance 2306.2.2 Mutual Inductance 2326.3 Energy and Forces in Magnetic Fields 2346.3.1 The Magnetic Energy Stored in an Inductor 2346.3.2 The Total Magnetic Energy of a System of Currents 2356.3.3 The Potential Energy of a Coil in a Field and the Force on the Coil 2376.3.4 The Total Magnetic Energy in Terms of the Fields B and H 2396.3.5 Non-linear Media 241* 6.3.6 Further Comments on Energy in Magnetic Fields. 2436.4 The Measurement of Magnetic Fields and Susceptibilities 2466.4.1 The Measurement of Magnetic Fields 2466.4.2 The Measurement of Magnetic Susceptibilities 248Problems 6 2507 Alternating Currents and Transients7.1 Alternating Current Generators 2537.2 Amplitude, Phase and Period 2567.3 Resistance, Capacitance and Inductance in A.C. Circuits 2577.4 The Phasor Diagram and Complex Impedance 2607.5 Power in A.C. Circuits 2667.6 Resonance 2687.7 Transients 274Problems 7 2808 Linear Circuits8.1 Networks 2828.1.1 Kirchhoffs Rules 2838.1.2 Loop Analysis, Node Analysis and Superposition 2868.1.3 A.C. Networks 2888.2 Audio-frequency Bridges 2918.3 Impedance and Admittance 2938.3.1 Input Impedance 2968.3.2 Output Impedance and Thevenin's Theorem 2978.4 Filters 2998.4.1 Ladder Networks 3018.4.2 Higher Order Filters and Delay Lines 3038.5 Transformers 3078.5.1 The Ideal Transformer 3088.5.2 Applications of Transformers. 3118.5.3 Real Transformers 312* Problems 8 3189 Transmission Lines9.1 Propagation of Signals in a Lossless Transmission Line 3249.2 Practical Types of Transmission Line 3299.2.1 The Parallel Wire Transmission Line 3299.2.2 The Coaxial Cable 3319.2.3 Parallel Strip Lines 3339.3 Reflections 335* 9.4 The Input Impedance of a Mismatched Line 338* 9.5 Lossy Lines 342Problems 9 34510 Maxwell's Equations10.1 The Equation of Continuity 34810.2 Displacement Current 35010.3 Maxwell's Equations 35610.4 Electromagnetic Radiation 359* 10.5 The Microscopic Field Equations 360Problems 10 36211 Electromagnetic Waves11.1 Electromagnetic Waves in Free Space 36511.2 Plane Waves and Polarization 36811.2.1 Plane Waves in Free Space 37311.2.2 Plane Waves in Isotropic Insulating Media 37511.3 Dispersion 37911.4 Energy in Electromagnetic Waves 38311.5 The Absorption of Plane Waves in Conductors and the Skin Effect 38811.6 The Reflection and Transmission of Electromagnetic Waves 39111.6.1 Boundary Conditions on Electric and Magnetic Fields 39211.6.2 Reflection at Dielectric Boundaries 39611.6.3 Reflection at Metallic Boundaries 399* 11.6.4 Polarization by Reflection 401* 11.7 Electromagnetic Waves and Photons 404Problems 11 40612 Waveguides12.1 The Propagation of Waves Between Conducting Plates. 40912.2 Rectangular Waveguides. 41512.2.1 The TE 01 Mode. 420* 12.2.2 Further Comments on Waveguides 42312.3 Cavities 426Problems 12 43013 The Generation of Electromagnetic Waves13.1 The Retarded Potentials 43313.2 The Hertzian Dipole 43613.3 Antennas 443Problems 13 45014 Electromagnetism and Special Relativity14.1 Introductory Remarks 45114.2 The Lorentz Transformation 45214.3 Charges and Fields as seen by Different Observers 45514.4 Four-vectors 45814.5 Maxwell's Equations in Four-vector Form 46114.6 Transformation of the Fields 46414.7 Magnetism as a Relativistic Phenomenon 46914.8 Retarded Potentials From the Relativistic Standpoint 473Problems 14 476Appendix A UnitsA.1 Electrical Units and Standards 477A.l.l The Definition of the Ampere 477A.l.2 Calibration and Comparison of Electrical Standards 479A.2 Gaussian Units 482A.3 Conversion between SI and Gaussian Units 485Appendix B Fields and Differential OperatorsB.l The Operators div, grad and curl 487B.2 Formulae in Different Coordinate Systems 489B.3 Identities 493Appendix C The Derivation of the Blot-Savart Law Solutions to Problems 497Solutions to Problems 497Further Reading 518Index 519