Historical research guide · 0706 · 1907
Über die Fortpflanzung ebener elektromagnetischer Wellen längs einer ebenen Leiterfläche und ihre Beziehung zur drahtlosen Telegraphie
J. Zenneck
In one minute
In 1907 Jonathan Zenneck, at the Technische Hochschule in Braunschweig, asked what a plane electromagnetic wave does when it runs along the flat surface of a conductor — and unlike the two people who had tried before him, he let the conductor be a poor one: damp soil, dry sand, rock. He solved Maxwell’s equations with the boundary conditions at that surface and got a wave bound to the interface rather than radiated away from it. It travels very close to the speed of light. It fades over kilometres along the ground while fading over centimetres into the ground. And near the surface its electric field is not vertical: over dry ground it tilts by tens of degrees and picks up a rotating component, so the tip of the field vector traces an ellipse through each cycle. Zenneck turned that into an engineering instruction — slant the receiving antenna — and the wireless engineer Graf von Arco wrote back to confirm that in practice it worked.
Connection
Chapter 10 is about fields that are guided rather than radiated, and this is the paper the whole surface-wave lineage rests on: the first exact solution for a wave bound to the boundary between the air and a conductor of arbitrary quality, written by the man whose name that wave now carries. It is also a working answer to the question of why long-wave stations reached across the sea and died over dry land, and it ends with the open problem — the rigorous boundary-value solution for an Earth of arbitrary conductivity — that Sommerfeld took up two years later. James and Kenneth Corum’s modern surface-wave patent, which builds its launching condition directly on Zenneck’s complex Brewster angle, is at /library/stm-26e7682d4c.
From the source
Zenneck sets up the general case that had not been done. Emil Cohn had treated a conductor with the electrical properties of a metal, and Karl Uller a well-conducting liquid such as seawater; Zenneck solves for a conductor of arbitrary and possibly far poorer conductivity, and asks for the influence not only of that conductivity but of the conductor’s dielectric constant, and of any conductivity of the air as well. With the wave travelling along the x-axis and the magnetic field along the y-axis, Maxwell’s equations plus the boundary conditions at the surface give a solution in which the field falls off away from the interface on both sides.Part A, opening; Section 1, Die Ausgangsgleichungen
The electric field near the surface is in general not a pure alternating field. A rotating component is always present alongside it, so over one period the tip of the resultant field vector traces an ellipse rather than a line. Where the conductor’s conductivity is not much below about ten to the minus twelve or minus thirteen in C.G.S. units, the field in air stands nearly perpendicular to the surface and inside the conductor nearly parallel to it, whatever the dielectric constant; where the conductivity is poorer and the dielectric constant small, the air-side field tilts strongly away from the normal and the rotating component grows.Section 3, Die Richtung des elektrischen Feldes, with Figures 2 to 6
Over water the field is vertical to within about six degrees, so nothing changes for a coastal station; over dry ground the direction of maximum electric amplitude departs from the vertical considerably, by about thirty-five degrees in one of the worked cases. Zenneck therefore instructs that a land station should slant its receiving antenna into that direction rather than hang it vertically: for the constants of that case a vertical antenna gives up about eighteen percent of the amplitude and a wire slanted the opposite way about sixty-six percent. Graf von Arco replied, when asked, that a slanted receiving antenna does in fact pick up more than a vertical one and that the indicated direction had always proved right in practice.Section 9, Das elektrische Feld an der Oberfläche der Erde, with Figures 9 and 10 and the footnote quoting Graf von Arco
The attenuation along the surface has a maximum at a particular conductivity, and the dielectric constant of the ground matters at least as much as its conductivity. Writing the distance in which the amplitude falls to one over e, Zenneck finds that with the dielectric constant of water, taken as eighty, that distance never drops below about four hundred kilometres — which is why absorption in seawater plays no part in a station’s range — while for a dielectric constant of two it falls to about one kilometre and for five to about two kilometres. That is the known collapse of range over long stretches of dry ground, and its cause is at least as much the low dielectric constant as the low conductivity.Section 4, Die Absorption der Wellen in der Fortpflanzungsrichtung, with Figure 7; Section 10, with Figure 11
The wave is bound to the surface, and the numbers say so twice over. Absorption on entering the conductor is enormously stronger than absorption along it: what is one kilometre for the wave running along the surface is about one centimetre for the wave going down into the conductor. And the propagation speed along the surface comes out very close to the speed of light in air, or a little above it — which Zenneck attributes to the radiation direction standing oblique to the surface — with the electric and magnetic intensities near enough in phase to be treated as in phase for qualitative purposes.Section 5, Absorption der Wellen beim Eindringen in den Leiter, with Figure 8; Section 6
Zenneck names his own open problem rather than hiding it. The wave he has solved for is a plane wave, and whether the waves a wireless transmitter actually sends take this form far from the sender could only be decided rigorously by solving, for an Earth surface of arbitrary conductivity, the problem Max Abraham had solved for a perfectly conducting one. Until that is done, he writes, the conclusions drawn for wireless telegraphy hang to some degree in the air, and he draws them faute de mieux, on the strength of the analogy with waves guided along wires. He weighs the day-versus-night range difference the same way, and concludes that air layers below six thousand metres cannot be responsible for it.Section 7, Die Verwendbarkeit der Resultate für die drahtlose Telegraphie; Section 11 d
The way in
https://doi.org/10.1002/andp.19073281003How to cite it
J. Zenneck (1907) Über die Fortpflanzung ebener elektromagnetischer Wellen längs einer ebenen Leiterfläche und ihre Beziehung zur drahtlosen Telegraphie doi:10.1002/andp.19073281003