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.