ELECTRICITY AND MAGNETISM

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1 THIRD EDITION ELECTRICITY AND MAGNETISM EDWARD M. PURCELL DAVID J. MORIN Harvard University, Massachusetts Щ CAMBRIDGE Ell UNIVERSITY PRESS

2 Preface to the third edition of Volume 2 XIII CONTENTS Preface to the second edition of Volume 2 XVII Preface to the first edition of Volume 2 XXI CHAPTER 1 ELECTROSTATICS: CHARGESAND FIELDS Electric charge 1.2 Conservation of charge 1.3 Quantization of charge 1.4 Coulomb's law 1.5 Energy of a system of charges 1.6 Electrical energy in a crystal lattice 1.7 The electric field 1.8 Charge distributions 1.9 Flux 1.10 Gauss's law 1.11 Field of a spherical charge distribution 1.12 Field of a line charge 1.13 Field of an infinite flat sheet of charge 1.14 The force on a layer of charge 1.15 Energy associated with the electric field 1.16 Applications

3 vi CONTENTS CHAPTER 2 THE ELECTRIC POTENTIAL Line integral of the electric field Potential difference and the potential function Gradient of a scalar function Derivation of the field from the potential Potential of a charge distribution Uniformly charged disk Dipoles Divergence of a vector function Gauss's theorem and the differential form of Gauss's law The divergence in Cartesian coordinates The Laplacian Laplace's equation Distinguishing the physics from the mathematics The curl of a vector function Stokes' theorem The curl in Cartesian coordinates The physical meaning of the curl Applications CHAPTER 3 ELECTRIC FIELDS AROUND CONDUCTORS Conductors and insulators Conductors in the electrostatic field The general electrostatic problem and the uniqueness theorem Image charges Capacitance and capacitors Potentials and charges on several conductors Energy stored in a capacitor Other views of the boundary-value problem Applications

4 CONTENTS VII CHAPTER 4 ELECTRIC CURRENTS Electric current and current density Steady currents and charge conservation Electrical conductivity and Ohm's law The physics of electrical conduction Conduction in metals Semiconductors Circuits and circuit elements Energy dissipation in current flow Electromotive force and the voltaic cell Networks with voltage sources Variable currents in capacitors and resistors Applications CHAPTER 5 THE FIELDS OF MOVING CHARGES From Oersted to Einstein Magnetic forces Measurement of charge in motion Invariance of charge Electric field measured in different frames of reference Field of a point charge moving with constant velocity Field of a charge that starts or stops Force on a moving charge Interaction between a moving charge and other moving charges CHAPTER 6 THE MAGNETIC FIELD Definition of the magnetic field Some properties of the magnetic field 286

5 viii CONTENTS 6.3 Vector potential 6.4 Field of any current-carrying wire 6.5 Fields of rings and coils 6.6 Change in В at a current sheet 6.7 How the fields transform 6.8 Rowland's experiment 6.9 Electrical conduction in a magnetic field: the Hall effect 6.10 Applications CHAPTER 7 ELECTROMAGNETIC INDUCTION 7.1 Faraday's discovery 7.2 Conducting rod moving through a uniform magnetic field 7.3 Loop moving through a nonuniform magnetic field 7.4 Stationary loop with the field source moving 7.5 Universal law of induction 7.6 Mutual inductance 7.7 A reciprocity theorem 7.8 Self-inductance 7.9 Circuit containing self-inductance 7.10 Energy stored in the magnetic field 7.11 Applications CHAPTER 8 ALTERNATING-CURRENT CIRCUITS 8.1 A resonant circuit 8.2 Alternating current 8.3 Complex exponential solutions 8.4 Alternating-current networks 8.5 Admittance and impedance 8.6 Power and energy in alternating-current circuits 8.7 Applications

6 CONTENTS ix CHAPTER 9 MAXWELL'S EQUATIONS AND ELECTROMAGNETIC WAVES "Something is missing" The displacement current Maxwell's equations An electromagnetic wave Other waveforms; superposition of waves Energy transport by electromagnetic waves How a wave looks in a different frame Applications CHAPTER 10 ELECTRIC FIELDS IN MATTER Dielectrics The moments of a charge distribution The potential and field of a dipole The torque and the force on a dipole in an external field Atomic and molecular dipoles; induced dipole moments Permanent dipole moments The electric field caused by polarized matter Another look at the capacitor The field of a polarized sphere A dielectric sphere in a uniform field The field of a charge in a dielectric medium, and Gauss's law A microscopic view of the dielectric Polarization in changing fields The bound-charge current An electromagnetic wave in a dielectric Applications CHAPTER 11 MAGNETIC FIELDS IN MATTER How various substances respond to a magnetic field 524

7 X CONTENTS The absence of magnetic "charge" The field of a current loop The force on a dipole in an external field Electric currents in atoms Electron spin and magnetic moment Magnetic susceptibility The magnetic field caused by magnetized matter The field of a permanent magnet Free currents, and the field H Ferromagnetism Applications CHAPTER 12 SOLUTIONS TO THE PROBLEMS Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Appendix A: Differences between SI and Gaussian units 762 Appendix B: SI units of common quantities 769 Appendix C: Unit conversions 774 Appendix D: SI and Gaussian formulas 778 Appendix E: Exact relations among SI and Gaussian units 789

8 CONTENTS XI Appendix F: Curvilinear coordinates 791 Appendix G: A short review of special relativity 804 Appendix H: Radiation by an accelerated charge 812 Appendix I: Superconductivity 817 Appendix J: Magnetic resonance 821 Appendix K: Helpful formulas/facts 825 References 831 Index 833 i

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