For an electron of mass m and charge e moving at time t with velocity v and acceleration d v /dt in an electric field of magnitude E, the accelerating force is proposed, in accordance with Newton’s second law of motion, as F = eE(c – v)/c = m(d v /dt). The vector c is the velocity of light and (c – v) is the relative velocity of the electrostatic force with respect to the moving electron. The electron may move in a straight line to reach the limiting speed c with F reducing to 0, or it can revolve in a circle at constant speed. The relativistic mass-velocity formula is shown to be correct for circular revolution only and that the mass in that formula is not a physical quantity but the ratio of electrostatic force (eE) to centripetal acceleration (v 2 /r) in a circle of radius r. This ratio can become infinitely large for motion in a circle of infinite radius, which is a straight line. An alternative electrodynamics is developed for an electron accelerated to the speed of light at constant mass and with emission of radiation. Radiation occurs if there is a change in the kinetic energy of an electron and, as such, circular revolution of an electron, round a central force of attraction, is made stable without recourse to quantum mechanics.

Keywords: Acceleration, electric charge, energy, force, mass, velocity

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