Terminal Speed of an Electron Accelerated by an Electric Field

Abstract

Musa D. Abdullahi

An electron of charge -e and mass m moving at time t with speed v and acceleration (dv/dt) in a straight line, in an electric field of magnitude E, comes under the influence of an impressed force -eE. The moving electron encounters a radiation reaction force eEv/c so that the accelerating force becomes -eE(1 – v/c) = -m(dv/dt), with constant mass m. It emits radiation with radiation power as (eEv^2)/c and reaches a terminal speed equal to that of light c, whereby the impressed force -eE becomes equal and opposite to the radiation reaction force and the acceleration reduces to zero. It is emission of radiation, not increase of mass with speed, that prevents an accelerated electron from going beyond the speed of light. Doing away with infinitely large masses of electrons moving at the speed of light in linear particle accelerators, should bring great relief to physicists all over the world

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