Energy Conservation in a Charged Retarded Field Engine

Prachi Sharma and Asher Yahalom ()
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Prachi Sharma: Faculty of Engineering, Department of Electrical & Electronic Engineering, Ariel University, Ariel 40700, Israel
Asher Yahalom: Faculty of Engineering, Department of Electrical & Electronic Engineering, Ariel University, Ariel 40700, Israel

Energies, 2025, vol. 18, issue 17, 1-48

Abstract: Energy conservation, rooted in the time invariance of physical laws and formalized by Noether’s theorem, requires that systems with space-time translational symmetry conserve momentum and energy. This work examines how this principle applies to a charged retarded field engine, where the rate of change of total energy—mechanical plus field energy—is balanced by the energy flux through the system’s boundary. Using electric and magnetic field expressions from a Taylor expansion to incorporate retardation effects, we analyze the energy equation order by order for two arbitrary charged bodies. Our results show that total energy is conserved up to the fourth order, with mechanical and field energy changes exactly offset by boundary energy flux. Consequently, the work done by the internal electromagnetic field precisely equals the engine’s gained mechanical kinetic energy, addressing the central focus of this study.

Keywords: electromagnetism; retardation; relativity (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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