# Inadequacies in the conventional treatment of the radiation field of moving sources - Mathematical Physics

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Abstract: There is a fundamental difference between the classical expression for theretarded electromagnetic potential and the corresponding retarded solution ofthe wave equation that governs the electromagnetic field. While the boundarycontribution to the retarded solution for the {\em potential} can always berendered equal to zero by means of a gauge transformation that preserves theLorenz condition, the boundary contribution to the retarded solution of thewave equation governing the {\em field} may be neglected only if it diminisheswith distance faster than the contribution of the source density in the farzone. In the case of a source whose distribution pattern both rotates andtravels faster than light {\em in vacuo}, as realized in recent experiments,the boundary term in the retarded solution governing the field is by a factorof the order of $R^{1-2}$ {\em larger} than the source term of this solution inthe limit that the distance $R$ of the boundary from the source tends toinfinity. This result is consistent with the prediction of the retardedpotential that part of the radiation field generated by a rotating superluminalsource decays as $R^{-1-2}$, instead of $R^{-1}$, a prediction that isconfirmed experimentally. More importantly, it pinpoints the reason why anargument based on a solution of the wave equation governing the field in whichthe boundary term is neglected such as appears in the published literaturemisses the nonspherical decay of the field.

Author: ** Houshang Ardavan, Arzhang Ardavan, John Singleton, Joseph Fasel, Andrea Schmidt**

Source: https://arxiv.org/