In this paper, we discussed the motion of charged particles in the external fields and the radiation of a system of two action reciprocal charges. Where we find that the motion of each charged particle, or precisely the motion of the moving charged particles in orbits has conical forms, and their foci are located in the center of inertia, and this is compatible with Kepler's problem in determining the motion of the planets. As we have shown, the results obtained are that a system consisting of two identical particles, or of different particles, with the same ratio (e / m) , can not radiate in a dipole approximation, and that the moving charge in a closed orbit continuously radiates energy. The differential cross section of particles scattering was calculated according to the Coulomb law, and the radiation value resulting from the incident of a beam of charged particles was finally calculated on a static charge (the braking radiation), where the radiation energy was found to be inversely proportional to the particle velocity as well as the cube with the radius of the radiation correction, and it is associated with the angle of scattering and the azimuth angle.