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

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The primary purpose of this work is to determine an equation of motion for the classical Lorentz model of the electron that is consistent with causal solutions to the Maxwell-Lorentz equations, the relativistic generalization of Newtons second law of motion, and Einsteins mass-energy relation. The work begins by reviewing the contributions of Lorentz, Abraham, Poincare, and Schott to this century-old problem of finding the equation of motion of an extended electron. Their original derivations, which were based on the Maxwell-Lorentz equations and assumed a zero bare mass, are modified and generalized to obtain a nonzero bare mass and consistent force and power equations of motion. By looking at the Lorentz model of the electron as a charged insulator, general expressions are derived for the binding forces that Poincare postulated to hold the charge distribution together. A careful examination of the classic Lorentz-Abraham derivation reveals that the self electromagnetic force must be modified during the short time interval after the external force is first applied. The resulting modification to the equation of motion, although slight, eliminates the noncausal pre-acceleration that has plagued the solution to the Lorentz-Abraham equation of motion. As part of the analysis, general momentum and energy relations are derived and interpreted physically for the solutions to the equation of motion, including hyperbolic and runaway solutions. Lorentz Electron, Relativistic Dynamics, Charged Sphere.

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  • Theoretical Mathematics

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