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

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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.

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Product Details

  • ISBN-13: 9780387978871
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 9/10/1992
  • Series: Lecture Notes in Physics , #11
  • Pages: 115

Table of Contents

1 Introduction and summary of results 1
2 Lorentz-Abraham force and power equations 11
3 Derivation of force and power equations 17
4 Internal binding forces 23
5 Electromagnetic, electrostatic, bare, measured, and insulator masses 35
6 Transformation and redefinition of force-power and momentum-energy 45
7 Momentum and energy relations 59
8 Solutions to the equation of motion 67
App. A Derivation and transformation of small-velocity force and power 121
App. B Derivation of force and power at arbitrary velocity 129
App. C Electric and magnetic fields in a spherical shell of charge 139
App. D Derivation of the linear terms for the self electromagnetic force 141
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