Relativistic Dynamics of a Charged Sphere: Updating the Lorentz-Abraham Model

by Arthur Yaghjian

Overview

"This is a remarkable book. […] A fresh and novel approach to old problems and to their solution." –Fritz Rohrlich, Professor Emeritus of Physics, Syracuse University

This book takes a fresh, systematic approach to determining the equation of motion for the classical model of the electron introduced by Lorentz more than 100 years ago. The original derivations of Lorentz, Abraham, Poincaré and Schott are modified and generalized for the charged insulator model of the electron to obtain an equation of motion consistent with causal solutions to the Maxwell-Lorentz equations and the equations of special relativity. The solutions to the resulting equation of motion are free of pre-acceleration and runaway behavior. Binding forces and a total stress–momentum–energy tensor are derived for the charged insulator model. Appendices provide simplified derivations of the self-force and power at arbitrary velocity.

In this Second Edition, the method used for eliminating the noncausal pre-acceleration from the equation of motion has been generalized to eliminate pre-deceleration as well. The generalized method is applied to obtain the causal solution to the equation of motion of a charge accelerating in a uniform electric field for a finite time interval. Alternative derivations of the Landau-Lifshitz approximation are given as well as necessary and sufficient conditions for the Landau-Lifshitz approximation to be an accurate solution to the exact Lorentz-Abraham-Dirac equation of motion.

The book is a valuable resource for students and researchers in physics, engineering, and the history of science.

Product Details

ISBN-13:	9780387260211
Publisher:	Springer New York
Publication date:	11/16/2005
Series:	Lecture Notes in Physics , #686
Edition description:	Second Edition 2006
Pages:	152
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

About the Author

Arthur D. Yaghjian works primarily as a research engineer in the area of electromagnetic theory. His work has led to the determination of electric and magnetic fields in material media, as well as to the development of exact, numerical, and high-frequency methods for predicting and measuring the near and far fields of antennas and scatterers in both the time and frequency domains. His contributions to the determination of the classical equations of motion of accelerated charged particles have found recognition in a number of texts such as the latest edition of Jackson's "Classical Electrodynamics." He has published two books, several chapters in other books, and about 50 archival journal articles, four of which received best paper awards. He is a Fellow of the IEEE and presently serves as an IEEE Distinguished Lecturer.

Table of Contents

Foreword.- Preface To The First Edition.- Preface To The Second Edition.- Introduction and Summary of Results.- Lorentz-Abraham Force And Power Equations.- Derivation of Force And Power Equations.- Internal Binding Forces.- Electromagnetic, Electrostatic, Bare, Measured, and Insulator Masses.- Transformation and Redefinition of Forcepower and Momentum-Energy.- Momentum and Energy Relations.- Solutions to The Equation of Motion.- Derivation and Transformation of Smallvelocity Force and Power.- Derivation of Force and Power at Arbitrary Velocity.- Electric and Magnetic Fields in a Spherical Shell of Charge.- Derivation of The Linear Terms for the Self Electromagnetic Force.- References.