Abstract

For an electron of mass m and charge ?e moving at time t with velocity v and acceleration dv/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(dv/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 (?v²/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 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.