A Simplified Trajectory for a Radiating Charge Moving in a Uniform Magnetic Field

Is shown that a radiating charge moving in a constant uniform magnetic field has an approximated trajectory that copies the Euler spiral. Is made a classical study for the motion with some plausible approximations. By comparing the graph of Cornu’s spiral, which is considered not from the initial point, but from an advanced point to satisfy the initial conditions, and the image obtained with the bubble chamber, a strong correspondence can be seen. This simple result is the springboard for an exact result in which starting from a formula adapted to overcome the inconsistencies of the current formulas for the radiation reaction force, one obtains again the same result presented in this article as a limiting case. This suggests that the new formula can describe the phenomenon of the radiation reaction force with more accuracy, combined with the fact that the new formula, which I hope to be able to present in a future article, provides in other cases of motion without the magnetic field, quite plausible results.