ELECTRO - DYNAMICS Yu. Novozhilov and Yu. A. Yappa MIR PUBLISHERS MOSCOW - O R T C S E C L I E M A N Y a D p p a Y A . u . Y d n a vv oo hh ii ll zz oo vv oo NN uu .. YY to. B. HOBOH<HnOB, to. A. flnna 311EKTPOA1I1HAM111KA H8~aTeJILCTBO «Hayxar MOCKB& ELECTRODYNAMICS Yu. V. Novozhilov and Yu. A. Yappa Translated from the Russian by v. I. Kisin Mir Publishers · Moscow First published 1981 Second printing 1986 TO THE READER Mir Publishers would be grateful for your comments on the content, translation and design of this book. We would also be pleased to receive any other suggestions you may wish to make. Our address is: Mir Publishers 2 Pervy Rizhsky Pereulok 1-110, GSP, Moscow, 129820, USSR Ha 4HZAUUC1:0M Jl8blXe ~ rnaBHaH peAaK~HH ~RaHKo-MaTeMaTUqeCKOHnUTepaTypY H8AaTenbCTBa cHayK8», 1.978 ' © English translation, Mir Publishers, 198t CONTENTS Preface .to the Russian Edition . 7 Preface to the English Edition . 9 Notation 10 Chlpter t. The Blslcs of Maxwell's Electrodynamics. • • . . . . . . 13 § 1. The Maxwell equations. Electromagnetic units . . . . . . . 13 § 2. The potentials of the electromagnetic field. Gauge invariance. Hertz vectors . . . . . . . . . . . . . . . . . . . . ~ . 27 § 3. Lawsgoverningthe variationofenergy,momentum;and angular momentum . 33 § 4. Properties of the Maxwell equations. Uniqueness of the solu tion in bounded regions. Boundaryconditions at the interface between two media . . . . . . . . . . . . . . . . . . • 38 Chapter 2. ReletlvlstlcElectrodynamics 45 § 5. The principleofrelativity. Lorentztransformations, and relat ivistic kinematics . . . . . . . . . . . . . . . . . . . 45 § 6. Relativistic particle dynamics . . . . . . . . . . . . .. 55 § 7. The re~ativistic Maxwell equations. The field strength. trans- formattons ............••........ 59 § 8. Relativistic equations of charge motion . . . . . . . . . 69 § 9*. Variational principle for electromagnetic field . . . . . . 75 § 10*. The Noether theorem. Relativistic differential and integral conservation laws for electromagnetic fields . . . . . . . 81 Chepter 3.·Stllllc Fields. Solution of the W.ve Eq on. aadldon Field 90 § 11. Electrostatic field . 90 § 12. Magnetostatic field generated by currents . • . . . . . • 98 § 13. Solution of the nonhomogeneous wave equation. The Lie- nard-Wiechert potentials . . . . • • • • • . . . . . . • 103 § 14. Field strength around a pointlike charge. Radiation field.: Uniform linear motion of a charge • • • • • • • . . . ito § 15*. Relativistic law of energy-momentum conservation for the electromagnetic field of a pointlike charge • . . . . . 116 § 16. Energy radiated by a moving charge • • • . . . . . . . . 123 § 17. Emission from bounded oscillating sources • . . . . . 131