One-piece Faraday generator: A paradoxical experiment from 1851

Abstract

In the conventional Faraday generator a conducting disk rotates in an axial magnetic field. If the disk is replaced by a cylindrical permanent magnet that supplies its own magnetic field, the effect is identical. It follows that any moving magnet generates an induced electromotive force due to the presence of its own field: this generalization leads to an apparent paradox in the case of translational motion for it implies the possibility that an observer in an inertial frame could measure his absolute velocity.

Unipolar Induction Revisited: New Experiments and the “Edge Effect” Theory

“…Applying now a well-known vectorial theorem (4) and recalling that has no divergence and that for constant linear velocity the second and third term of the right hand become zero, the previous theorem reduces to (5) Applying (5) to the last term of (3), finally leads to field is what will be called in this paper the "edge effect". Its function is to combine with the positive that still is operative along the wire IR when it moves with the magnet, so that the net result is zero as seen by experience in the rectilinear case 8.…”

“…a) Anticipation of Similar Solutions: Crooks et al [4] have certainly described the edge effect as a step function whose surface integration leads to BvL in straight line motion and whose negative sign is predictable by Lenz's law. On the other hand, Panofsky and Phillips [8] are contented with briefly quoting the vectorial theorem ((4) above) and concluding that is "also the effective electric field in the moving medium".…”

“…It will be seen that in rotation there is no need of relative motion between magnet and conductor for induction to occur, whereas in translation relativity of motion is crucially required, as stated by Einstein in 1905 [18]. Rarely this comparison is found in the literature although Crooks et al [4] came closest to it. They, however, do not present realistic experiments to test, and explain, what will be called in this paper the "edge effect".…”

“…Only the parameter is constant and can be taken out of the last integral in (13). A possible way to proceed is to use the delta function as done by Crooks et al [4], but in two dimensions and in polar coordinates . Thus, shifting the differential of (13) to the B field and leaving the area as after the magnet has rotated some angle the integral becomes (14) To calculate we imagine the magnet rotating as shown in Fig.…”

“…Perusal of the literature after Miller's book still shows a great variety and even opposition between authors concerning Faraday's generator of 1832 [3], sometimes labeled as "Faraday's paradox", others as Faraday's "paradoxical generator" [4].…”