On the radiation from point charges

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Abstract
An alternative derivation of the radiation field of a point charge is presented. It starts with the Fourier components of the current produced by the moving charge. The electric field is found from the vector wave equation. Each step in the integration permits physical interpretation. The retarded time appears very naturally in this derivation. The interpretation of the present derivation is that a charge at constant velocity v̄(‖v̄‖<c) does not radiate, not because it is unaccelerated, but because it has no Fourier components synchronous with waves traveling at the speed of light. Of course, Cherenkov radiation in a medium, in which the velocity of electromagnetic propagation is less than c, is the classic example of radiation by a charge moving at constant velocity.

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