Abstract
AbstractGeneral expressions for the momentum and energy of the moving charge are derived from the equation of motion. The reversible kinetic momentum-energy, the reversible Schott acceleration momentum-energy, and the irreversible radiation momentum-energy are separated in both three and four-vector notation. After the application of an external force to the charged particle, all the momentum-energy that has been supplied by the external force has been converted entirely to kinetic and radiated momentum-energy. However, while the external force is being applied, the momentum-energy is converted to Schott acceleration momentum-energy, as well as kinetic and radiated momentum-energy. It is confirmed that the conservation of momentum-energy is not violated by a charge in hyperbolic motion (relativistically uniform acceleration), or by the homogeneous runaway solutions to the equation of motion. By writing the three-vector equation of motion in an especially compact form, it is proven that the only possible solution to the equation of motion for relativistically uniform acceleration is rectilinear “hyperbolic motion” of the charge under a constant externally applied force in some inertial reference frame. This is the only externally applied force for which the radiation reaction force is zero and the Lorentz-Abraham-Dirac equation of motion reduces to the relativistic version of Newton’s second law of motion.KeywordsHyperbolic motionKinetic momentum-energyRadiation momentum-energyRunaway motionSchott momentum-energy
Published Version
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