Classical electrodynamics of an accelerated extended charge

The extent of an electric charge is considered under the assumption that the structure of the charge at rest is spherically symmetric and the current vector has a linear dependence on the acceleration. An exact expression for the electromagnetic field of the charge is obtained that depends on the specific form of the charge distribution. For the cases when the particle velocity does not considerably change over the time it covers the distance of the order of its own size, approximations are developed that depend on the charge distributions through its low-order momentums. The Lorentz-Abraham-Dirac expression is rigorously proven for radiation friction: the initial expression and the conditions under which the expression can be derived are identified. The radiation field is also studied and it is demonstrated that in some cases of great accelerations the radiation virtually vanishes. Methods for the further development of the theory are pointed out as applied to more general forms of the current vector (dependence of the charge structure on the acceleration, consideration of random factors, etc.).