Historical research guide · 0687 · 2023
The importance of Weber-Maxwell electrodynamics in electrical engineering
Steffen Kühn
In one minute
Steffen Kühn rewrites the force between moving charges as a wave equation that combines Weber’s direct-force picture with Maxwell’s equations. In his formulation, a magnetic field is not a separate ingredient: the force on a moving charge near a current-carrying wire comes from summing interactions with the wire’s ions and electrons. At small drift speeds and after a second-order expansion, that calculation recovers the familiar magnetic-force result. Kühn derives conservation of total momentum for isolated charges and states the conditions needed for energy and angular-momentum conservation. The latter requires a central pairwise force, which he says holds only when propagation delay can be neglected. The paper points to open circuits as places to compare predictions and leaves near-light-speed motion unresolved.
Connection
Chapter 10 asks how electric and magnetic forces can be described. Kühn’s direct-force formulation gives the same result in the closed-loop cases he discusses, while open circuits such as a capacitor gap offer a place to compare predictions.
From the source
Weber-Maxwell electrodynamics compresses all four of Maxwell’s equations and the Lorentz force into a single three-dimensional wave equation for the force between two point charges; in the rest frame of the receiver it differs from the wave equation of Lorentz-Einstein electrodynamics only by an additional Lorentz factor, whose sole purpose is to renormalise the force so that the concept of the magnetic field becomes unnecessary.Abstract; Section II, Eqs. (1)-(3) and the discussion following Eq. (8)
Newton’s third law holds under all circumstances in this formulation — including when electromagnetic waves are present and the two charges are far enough apart that the finite propagation speed of the force matters — which Kühn proves by exchanging source and receiver in the wave equation.Section II, Eq. (12)
Kühn derives conservation of total momentum for isolated point charges from equal-and-opposite pairwise forces. His energy proof also requires a compatible potential energy, while angular-momentum conservation requires momentum parallel to velocity and a central pairwise force; he states that the central-force condition applies when propagation delay is unimportant.Section III A-E, especially Eq. (43), Eq. (51) and Section III E's conditions
In an isolated system the electromagnetic wave possesses neither energy nor momentum but only mediates them between particles of matter; a wave appears to carry momentum only when a subsystem is considered — the receiver without the transmitter — because the transmitter simultaneously takes the compensating recoil elsewhere.Section II, discussion following Eq. (12); Section III C
Kühn models the force on a moving charge beside an infinitely long wire by integrating interactions with its resting ions and drifting electrons. For small electron drift speed, a second-order expansion in the test charge’s speed recovers the standard magnetic-force expression without the Fechner hypothesis.Section IV, Eqs. (52)-(54)
Kühn argues that symmetry cancels the Weber-specific force components in the closed conductor-loop cases he discusses; an open gap such as a capacitor can expose different predictions. He leaves the application of Weber–Maxwell electrodynamics to charges moving near light speed, including accelerator and fusion settings, for further work.Section IV, closing paragraphs; Section V, Summary and conclusion
The way in
https://doi.org/10.36227/techrxiv.21776546How to cite it
Steffen Kühn (2023) The importance of Weber-Maxwell electrodynamics in electrical engineering doi:10.36227/techrxiv.21776546