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Poynting: accounting for energy transfer in the electromagnetic field

Poynting 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.

What is recorded here?

Poynting 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. A 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.

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Scientific scope

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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People and systems

J. H. Poynting

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English catalogue narrative

Poynting: accounting for energy transfer in the electromagnetic field

Poynting 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.

A 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.

Scientific scope

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.

People and systems

J. H. Poynting

Original sources