Historical research guide · 0761 · 2022
Resolving the paradox of unipolar induction: new experimental evidence on the influence of the test circuit
Christof Baumgärtel · Simon Maher
In one minute
Spin a conducting disc next to a magnet and a voltage appears across the disc. Spin the magnet alone and nothing happens. Spin both together and the voltage comes back. That is Faraday’s paradox, and physicists have argued for nearly two centuries about whether a magnet’s field turns with it. Christof Baumgärtel and Simon Maher at the University of Liverpool built the piece of apparatus everyone had left out: a measuring circuit that can rotate too. Magnets, brass disc and a circuit board carrying its own amplifier and indicator lamp each sit on their own bearing, so all eight combinations of what spins and what stays still can be tested. Their finding is that the return wire is not a bystander — spin the measuring circuit alone and a voltage appears in it, growing in step with the speed of rotation. Once the whole loop is counted, the paradox dissolves; whether the field itself turns remains open.
Connection
Chapter 10 is about the parts of electromagnetism that are usually treated as bookkeeping — the vector potential, the return path, the direct action between charges — turning out to carry the physics. This is a clean modern instance: the closing wire, left out of the textbook account for 190 years, is where the induction is seated. The authors also press the question chapter 2 keeps asking, whether the field is a real physical entity or a map of possible interactions, and they name the experiment that could answer it.
From the source
The classic three cases of the Faraday generator are reproduced: with the disc rotating and the magnet still a voltage appears across the disc; with the magnet rotating alone none does; with disc and magnet turning together the voltage returns. The apparent paradox arises only when a magnet is rotated about its own axis of field symmetry, not for rectilinear motion, a horseshoe magnet or a quadrupole.Introduction, cases (i) to (iii)
The authors built the first apparatus in which the measurement circuit and its closing wire can themselves be rotated: two neodymium ring magnets, a brass disc and a circuit board carrying an instrumentation amplifier and indicator lamp, each on its own bearing on a lathe shaft, so that all eight combinations of what turns and what is held still can be tested.Apparatus; Figures 2 and 3
A voltage is induced in the closing wire alone. In cases 5 and 6, where only the measurement circuit rotates, the lamp lights for one direction of rotation and, with the amplifier polarity reversed, for the other; adding magnets behind the closing wire brightens it, and its measured intensity rises linearly with rotation rate, fitted by an intensity of 2.05 × 10⁻⁴ times the angular speed minus 0.0177, with an R-squared of 0.967.Results; Table 3; Figure 6
Analysed across all eight configurations, the moving-field picture, the stationary-field picture and Weber direct action predict exactly the same outcomes, differing only in which part of the circuit they say is polarised; all three agree that a voltage appears when the disc and the closing wire are polarised differently.Theoretical analysis: influence of the closing wire; Table 1
It is the relative motion between the disc and the closing wire that determines the appearance of an electromotive force, not the rotation of the magnet — so once the whole circuit is included in the analysis, unipolar induction is not a paradox and not an exception to the flux rule.Discussion; Conclusion
Whether the field co-rotates with the magnet cannot be decided from these data, because in the two mixed cases the seat of induction cannot be isolated; the authors propose a one-piece Faraday generator read by a non-contact or far-field electric measurement as the experiment that could settle it, and ask whether the field is a physical entity at all.Discussion, paragraphs on Figure 7; Conclusion
The way in
https://doi.org/10.1038/s41598-022-21155-xHow to cite it
Christof Baumgärtel, Simon Maher (2022) Resolving the paradox of unipolar induction: new experimental evidence on the influence of the test circuit doi:10.1038/s41598-022-21155-x