Historical research guide · 1018 · 2021
Experimental investigation of an unusual induction effect and its interpretation as a necessary consequence of Weber electrodynamics
Steffen Kühn
In one minute
Steffen Kühn built a small experiment to look for a force that modern electromagnetism says cannot exist. In the standard picture, the electric force on a charge does not care how fast the charge is moving, and the magnetic force always pushes sideways — so no electromagnetic force can push a charge along its own direction of travel in proportion to its speed. Kühn put a gas-discharge tube, with electrons drifting through it at about three quarters of a percent of the speed of light, alongside a small comb-shaped capacitor driven between twenty and sixty megahertz. With the tube’s electrons moving, an extra voltage appeared in the tube, and it grew in a straight line with frequency. That behaviour is exactly what Ampère’s original 1822 force law and Weber electrodynamics predict, and Kühn’s calculation of the size — about fourteen picovolts per hertz against about eleven measured — lands close. He is careful: this is an indication, and he names the experiments that would settle it.
Connection
Chapter 10 is about the parts of electromagnetism that the textbook field picture leaves out — the vector potential, longitudinal effects, and forces that act along the direction of motion rather than across it. This is a bench measurement aimed squarely at that gap, and chapter 1's evidence ladder is where it belongs: a small, cheap, repeatable experiment whose author states plainly what would confirm it and what would refute it.
From the source
Kühn’s formal claim, which does not depend on his experiment: the original form of Ampère’s force law is not fully compatible with the Biot-Savart law and modern electrodynamics, ’because modern electrodynamics, based on the Lorentz electromagnetic force, cannot describe a force component that is both proportional to the speed of the test charge and parallel to the direction of motion’, whereas Ampère’s original law does contain such components. ’This means that any claim that Ampère’s force law and Lorentz force would be compatible must be clearly rejected for purely formal reasons.’Section 4, Summary and conclusion, first conclusion
Weber’s law is derived here from a single strikingly simple starting point: the potential energy between two point charges is the ordinary Coulomb energy divided by the Lorentz factor of their relative radial speed — the speed with which they approach or recede along the line joining them. Expanding that for small relative speeds gives Weber’s 1848 potential and his 1846 force law, and Kühn notes that Ampère’s original force law follows from Weber’s law without additional assumptions, so that ’one could work without a vector potential, magnetic field, or Lorentz force’.Section 1, Introduction, equations 3 to 8 and the paragraph following equation 8
The experiment sets a cold-cathode fluorescent lamp tube beside one plate of a 37 picofarad comb-shaped capacitor on a small printed circuit board. The capacitor is driven with a 2.5 volt sine wave stepped from 20 to 60 megahertz; the tube’s electrons drift at roughly 0.0076 of the speed of light. Switching the tube’s high voltage on — that is, setting the charge carriers in motion — raised the measured amplitude above the same run with the high voltage off, and the difference between the two curves rises linearly with frequency.Sections 2.2 and 2.3, Figures 5 and 6
The size matches. Working from Ampère’s original force law, the predicted induced amplitude is a quarter of the capacitance per metre multiplied by the plate separation, the vacuum permeability, the drive amplitude, the carrier speed and the angular frequency; with the experiment’s own parameters and all 35 capacitor teeth this gives about 13.9 picovolts per hertz, while the straight-line fit to the measurement gives about 11.1 picovolts per hertz — a relative error of only 0.2, which Kühn says would shrink further if the tube length and the lateral offsets of the strip lines were taken into account.Section 3.3, equation 32 and the two paragraphs following it
Kühn works through the alternative explanations himself and reports why each fails: a curved carrier path would produce a signal at twice the drive frequency and no such harmonics were seen; a change in the tube gas permittivity on ignition would lower the antenna sensitivity, not raise it, as a soldered-in copper wire confirmed; and reversing the high-voltage polarity is not expected to change the amplitude because the two contributions stay ninety degrees apart in phase either way.Section 3.4, Objections
The author states the limit of his own result and names the next measurement: ’The experiment performed in this article does not yet provide a final proof that the postulated force actually exists. The results instead should be understood as an indication that such a force could exist, and that further experiments are worthy and necessary.’ To settle it he asks for a repeat with a tube whose electron speed can be adjusted, or with a superconductor, where the carrier speed can also be varied.Section 3.4, opening paragraph; Section 4, second conclusion
The way in
https://doi.org/10.36227/techrxiv.16535331.v1How to cite it
Steffen Kühn (2021) Experimental investigation of an unusual induction effect and its interpretation as a necessary consequence of Weber electrodynamics doi:10.36227/techrxiv.16535331.v1