Abstract
An exactly solvable two-body problem dealing with the Lorentz–Dirac equation is constructed in this paper. It corresponds to the motion of two identical charges rotating at opposite ends of a diameter, in a fixed circle, at constant angular velocity. The external electromagnetic field that allows this motion consists of a tangential time-independent electric field with a fixed value over the orbit circle, and a homogeneous time-independent magnetic field that points orthogonally to the orbit plane. Because of the geometrical symmetries of the charges’ motion, in this case it is possible to obtain the rate of radiation emitted by the charges directly from the equation of motion. The rate of radiation is also calculated by studying the energy flux across a sphere of a very large radius, using the far retarded fields of the charges. Both calculations lead to the same result, in agreement with energy conservation.
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