Momentum Conservation in a Charged Retarded Field Engine

Addressing the potential conflicts between momentum conservation laws and retardation requires a comprehensive understanding of both principles within the context of specific physical systems and theoretical frameworks. Indeed it was claimed that a relativistic engine is impossible due to the lack of linear momentum conservation. The purpose of this work is to settle this issue by demonstrating that linear momentum is indeed conserved for a charged retarded field engine. Earlier research has already introduced the concept of a charged retarded engine. The system gains mechanical momentum and energy when it is subjected to a total force for a certain amount of time. If retardation is taken into account a total force is present even if no external force affects the system, thus momentum seems to appear from nowhere violating the law of momentum conservation. However, momentum is indeed conserved as the present work demonstrates. We present a mathematical proof that the momentum is conserved in a time dependent electromagnetic retarded motor. The expression of field momentum comes out to be equal and opposite to the mechanical momentum gained by the material system as obtain in . This calculation of charged relativistic engine is an extension work of papers published earlier , which explored a non-charged relativistic engine. We prove that the total momentum in a relativistic motor including both material and electromagnetic linear momentum is indeed conserved as dictated by Noether’s theorem.