Historical research guide · 1151 · 1884

On the Transfer of Energy in the Electromagnetic Field

J. H. Poynting

In one minute

This is the paper that says where a circuit's energy actually travels. Poynting sets out to answer one question — by what path does the energy that appears as heat or work in a circuit get from the battery to the lamp? — and proves a general law: energy moves perpendicular to the plane containing the electric and magnetic force, at a rate per unit area equal to the two intensities multiplied together with the sine of the angle between them, divided by four pi, in the sense of a right-handed screw turned from the electric to the magnetic direction. Because the flow is perpendicular to both, it runs along the equipotential surfaces, and the lines of flow are where the electric and magnetic level surfaces cut each other. He then works the law through seven ordinary cases, and reaches the conclusion the paper is remembered for: none of a current's energy travels along the wire. It converges on the wire from the space around it.

Connection

Chapter 6 opens its account of where a circuit's power comes from with this paper, and until now cited it by name with nothing behind it. Everything the chapter calls settled in that section is here in Poynting's own words: that the energy is in the surrounding medium, that it enters through the conductor's surface, and that the seat of the electromotive force is where energy leaves the circuit rather than where it enters. Note what is and is not in the paper — Poynting accounts for the flow that crosses a chosen surface, and the later reading that splits the field into an intercepted part and a larger part that sweeps past is a reading of this solution rather than a result stated in it.

From the source

The law itself. Energy moves at any point perpendicularly to the plane containing the lines of electric force and magnetic force; the amount crossing unit area of that plane per second is the product of the two intensities multiplied by the sine of the angle between them and divided by four pi; and the direction of flow is that in which a right-handed screw would move if turned from the positive direction of the electromotive intensity to the positive direction of the magnetic intensity. It follows at once that the energy flows along the electric level surfaces and along the magnetic level surfaces, so that where both exist their lines of intersection are the lines of flow of energy.Introductory statement, p. 344, and the interpretation of the surface integral, pp. 348–349
How it is proved. Starting from Maxwell's expressions for the electric and magnetic energy per unit volume, Poynting differentiates the total energy inside a fixed closed surface with respect to time, substitutes the displacement current for the difference between the true current and the conduction current, replaces the total current by the curl of the magnetic intensity, and integrates the resulting volume integral by parts. What is left is an integral over the bounding surface alone. The equation then asserts that the gain per second in electric and magnetic energy within the surface, together with the work done by the electromagnetic forces and the energy the conductors turn into heat, is exactly what passes inward through the surface.General account, pp. 344–345; full mathematical proof, pp. 345–348, equations (1) to (7)
Application 1, the straight wire, and the sentence the paper is remembered for. Near a current-carrying wire the magnetic lines are circles about the axis and the electric lines run along it, so the flow is inward along the radius; across the end sections nothing flows, because they contain no component of the electromotive intensity. Poynting checks the bookkeeping directly: the energy entering through the surface of a length of wire per second works out to the current multiplied by the difference of potential between its ends, which by Ohm's law is the current squared multiplied by the resistance — Joule's law. He concludes that none of the energy of a current travels along the wire, but that it comes in from the non-conducting medium surrounding it, and is transformed into heat as it crosses successive layers until nothing is left by the time the centre is reached, where there is no magnetic force and so no energy passing.Applications, (1) A straight wire conveying a current, pp. 350–351
Applications 2 and 3, where energy leaves a circuit rather than entering it. In the slow discharge of a condenser through a fine wire, the electromotive intensity between the plates opposes the current while the magnetic intensity bears the same relation to it as in the wire, so by the screw rule the energy moves outwards from the space between the plates, travels along the equipotential surfaces, and converges again on the wire where those surfaces cut it. A circuit containing a voltaic cell behaves the same way: the energy diverges from the contact of the acid with the zinc, where the chemical energy is given up, some of it converging on the acid and on the copper surface and the rest spreading out to converge on the rest of the circuit. Drawing the level surfaces at equal potential differences, equal amounts of energy travel out per second between successive pairs of them.Applications (2), pp. 351–352, and (3), pp. 352–354
Applications 4 to 7, the thermoelectric circuits, the motor, induced currents and light. At a hot junction the heat is converted into electric and magnetic energy which moves outwards, some of it converging on the two metals to be turned back into heat by Joule's law and some on the cold junction to produce the Peltier heating. Poynting suggests the Thomson effect is better described not as an absorption or development of heat by the current but as a movement of energy outwards or inwards according to whether the electromotive intensity in the unequally heated metal opposes or agrees with the current. With a motor in the circuit, as the motor's speed rises the current falls, fewer level surfaces cut the rest of the circuit and more converge on the motor; in the limit all of them converge on it, the efficiency is perfect, and the rate of doing work is infinitely slow. Around a secondary circuit carrying no induced current the energy simply streams round it as a liquid streams round an obstacle; a change in the primary redistributes the field, and the energy that then moves through the secondary is the induced current. The last application is light: for a plane wave passing on unchanged, the energy in a unit cube with one face in the wave front must all cross that face in one over the velocity of a second, and equating the rate at which energy crosses the face to the energy inside the cube, with the circuital relations between the two intensities, gives the velocity as one divided by the square root of the permeability multiplied by the specific inductive capacity — and makes the magnetic energy equal to the electric energy. Poynting adds that this is the greatest velocity at which the two energies can travel together, reached only when the intensities are at right angles and the two energy densities are equal.Applications (4), pp. 355–357; (5), pp. 357–358; (6), p. 358; (7), pp. 358–360
The conclusion, and the honest limit he puts on it. A current in a conductor is to be regarded as consisting essentially of a convergence of electric and magnetic energy from the medium upon the conductor and its transformation there into other forms, while the current through a seat of so-called electromotive force is a divergence of energy from the conductor out into the medium. Poynting is explicit that he expects no new experimental test from this: the law is a deduction from Maxwell's equations, which were built to express the known facts including induction in secondary circuits, so it must agree with them, and no further proof is to be hoped for until some method is discovered of testing what goes on in the dielectric independently of the secondary circuit.Concluding remarks, pp. 360–361

The way in

https://en.wikisource.org/wiki/On_the_Transfer_of_Energy_in_the_Electromagnetic_Field

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

Received 17 December 1883, read 10 January 1884, communicated by Lord Rayleigh, and printed as paper XV of Philosophical Transactions volume 175, pages 343 to 361. John Henry Poynting died in 1914, so the work is out of copyright everywhere by age; the publisher's own modern scan is paywalled as a matter of hosting, not of rights, and was refused a fetch on 2026-09-12. The text below was read from the Wikisource transcription of the scanned volume, all nineteen page units of Index:PoyntingTransfer.djvu, every one of them at proofread level, which is a page-by-page transcription of the printed original rather than a summary of it. Poynting's displayed equations are given here as named results in words, in the same way the 1903 Whittaker sheet handles its formulae, because a re-typeset equation is a second chance to introduce an error the original never had; the symbols and their definitions are carried, and the complete original with its algebra is in the linked transcription and in the Internet Archive scan of the volume. Figures 1 to 6, which are line drawings of equipotential surfaces around a wire, a condenser, a cell, two thermoelectric circuits and a Thomson-effect circuit, are described rather than reproduced.

How to cite it

J. H. Poynting (1884) On the Transfer of Energy in the Electromagnetic Field doi:10.1098/rstl.1884.0016

Where it sits in the curriculum

Energy from the vacuum