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Classical electrodynamics basically assumes that a charged particle is a point charge, whose size is infinitesimal. This assumption caused a lot of problems with the radiation reaction (also called the self-force), by which a radiating particle feels friction. For example, Lorentz-Abraham-Dirac (LAD) model, which is the earliest theory about radiation reaction based on a point charge, leads to unphysical solutions such as runaway solutions and preacceleration. It has been tried to modify LAD model, and the most successful result was Landau-Lifshitz (LL) model, which also interpret well the recent experimental data of radiation reaction from laser-plasma interactions. However, even LL model has some problems, and particularly it cannot explain the radiation reaction of a uniformly accelerated charge. In this talk, we assume that the size of a particle is finite but the particle itself is completely indistinguishable from a point charge. By this assumption, we calculate the self-force of this particle undergoing uniform acceleration and uniform circular motion. The calculations show that the self-force of uniform acceleration can increase the effective mass of the particle, and it explain why a uniformly accelerated particle needs more energy to radiate. The calculations also indicate that the self-force of uniform circular motion only depends on the acceleration at the retarded time. In addition, we propose that there is a classical limit of the acceleration, and by combining it with the Schwinger limit we suggest that the classical radius of a particle is somehow related to the reduced Compton wavelength.
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