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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, PoincarÃ© 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.
|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|