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        "description": "The derivation uses Maxwell’s stated medium-energy and constitutive model; stationary-matter and moving-matter work terms must not be conflated. The original uses historical units and a 1/(4*pi) factor, not verbatim modern SI E cross H. Ohmic wire and slow-discharge examples, thermoelectric assumptions and uniform plane-wave cases have their own restrictions. The cell-potential interpretation is explicitly uncertain, and a proposed dielectric probe is prospective, not a completed experiment. Ideal motor efficiency reaches unity at a zero-power limit, not a practical perpetual-motion result. Conservation fixes a divergence and does not alone certify unique microscopic energy paths. Quantum theory, arbitrary dispersive/nonlinear media and all later power engineering are excluded. The complete derivation and its formulas have not been independently certified here.",
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      "statement": "# Poynting: accounting for energy transfer in the electromagnetic field\n\nPoynting derives a local electromagnetic energy balance from Maxwell’s theory and represents field-energy transport by a cross product of electric and magnetic intensities, illustrating how power reaches circuits and waves.\n\nA powered wire heats up, but where does its energy enter? This paper turns the surrounding electromagnetic field into an explicit energy-accounting system. It derives a surface-flux expression and illustrates inward energy flow around a straight resistive wire, capacitor discharge, motors and waves. The result connects a circuit’s supplied power to field energy entering a region and energy converted there into heat or work. The field theory is inherited from Maxwell; the contribution is its organized energy-transport account.\n\n## Scientific scope\n\nThe derivation uses Maxwell’s stated medium-energy and constitutive model; stationary-matter and moving-matter work terms must not be conflated. The original uses historical units and a 1/(4*pi) factor, not verbatim modern SI E cross H. Ohmic wire and slow-discharge examples, thermoelectric assumptions and uniform plane-wave cases have their own restrictions. The cell-potential interpretation is explicitly uncertain, and a proposed dielectric probe is prospective, not a completed experiment. Ideal motor efficiency reaches unity at a zero-power limit, not a practical perpetual-motion result. Conservation fixes a divergence and does not alone certify unique microscopic energy paths. Quantum theory, arbitrary dispersive/nonlinear media and all later power engineering are excluded. The complete derivation and its formulas have not been independently certified here.\n\n## People and systems\n\nJ. H. Poynting\n\n\n\n## Original sources\n\n- [Poynting: accounting for energy transfer in the electromagnetic field — original article scan](https://fnorio.com/0166Poynting_vector/Poynting_1884/Poynting_1884_Phil_Trans_175_343%EF%BD%9E361.pdf)\n",
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