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1. Unipolar or acyclic induction.
Possibly, there has been no simpler, more curious and polemical experiment since the beginnings of electromagnetism than Faraday’s rotating magnet and disc. For their simplicity and beauty they have always attracted the attention of the physicist.
According to Poincaré “The most curious electrodynamics experiments are those where a continuous rotation takes place, called unipolar induction experiments.”1
Einstein, in his first paper “On the electrodynamics of moving bodies,” states that: “It is known that Maxwell’s electrodynamics –as usually understood at the present time– when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena”. “Furthermore it is clear that the asymmetry mentioned in the introduction as arising when we consider the currents produced by the relative motion of a magnet and a conductor, now disappears. Moreover, questions as to the “seat” of electrodynamic electromotive forces (unipolar machines) now have no point.”2
It would seem the Faraday disc contributed to the development of the Theory of Relativity.
When studying unipolar induction back 1961, and finding the conducting spiral to be a universal unipolar generator I imagined that this must have been known since the beginnings of electromagnetism. In that year I had begun my Ph. D. course in Physics at Grenoble University and found to my surprise that the conducting spiral was unknown to my professors of electromagnetism. They suggested that I choose this for a second subject for my doctoral thesis3. It turned out to be very polemical, for as is well-known, unipolar induction continues to be the object of discussions and publications. On completing my thesis, the Board of Examiners recommended my second subject for publication; something I was only able to do years later, for in the opinion of the journal’s referee the conducting spiral was but a “mind experiment” and couldn’t possibly revolve. Only on checking the experiment (presumably), was the article accepted. This publication4 had involved considerable difficulties and scarce attention. To start with, I - the supposed discoverer - had failed to grasp the significance of the spiral. Curiously, this experiment, as straightforward and beautiful as the Faraday Disc, is just as paradoxical. Twenty-seven years after publishing my article I began my studies of unipolar induction anew with a series of experiments on conducting spirals which led me to a new understanding of electromagnetic induction, the Faraday Disc and the conducting spiral itself, establishing a new analogy between mechanics and electromagnetism. In November 1998, I attempted to publish these findings in the same journal which in 1970 had published my first article, only to have it rejected out of hand by the editor who alleged “articles announcing new theoretical results or experiments are not accepted in this journal”. Maybe he should have added: especially if they come from an unknown third-world Physicist, for this publication continues to carry articles on Faraday’s Induction Law and the Lorentz Force 5, 6, 7, 8, all of which deal with the old question as to how and where emf is generated in the Faraday Disc. Regarding the substance of the matter, some authors are of the opinion that the revolving magnet and the Faraday Disc are exceptions to Faraday’s Induction Law or flux rule9, and assure us that unipolar induction is due to the Lorentz Force, others deny any exceptions10, and still others see exceptions to the Lorentz Force11.
The difficulties in understanding the Faraday Disc derive from Faraday’s Induction Law and the equation F = il x B, which defines B and allows it to be measured. This assumes that magnetic induction B, generated by the circuit to which the segment l belongs, is negligible with regard to B. The emf and torque generated in the Faraday Disc depend on the shape of the circuit that connects the disc, giving rise to an “absolute – relative” duality of emf and Lorentz Force, which in turn, occasions different interpretations. This duality becomes much more evident in the conducting spiral and when the symmetry of the Faraday Disc is enhanced.
Some paradoxical experiments in unipolar induction which make use of the unique geometry of the spiral are described in this article. These experiments show that the paradoxes and discrepancies that arise with unipolar induction are resolved when the following analogies between mechanics and electromagnetism are established:
a) Charges, in the same way as mass, have a dual nature,
inert and gravitational, in each of these pairs neither
element is independent of the other.
b) In electromagnetic interaction among charges, both
mechanical and electromagnetic angular moments are
conserved.
c) Electromagnetic induction is due to the variation and
conservation of the angular moments of mass and
charge.
d) The possible ways of varying the electromagnetic
angular moment of a current in a circuit correspond to
the forms of electromagnetic induction.
e) The deformation of a circuit by electromagnetic forces tends to diminish the rate of change of the electromagnetic angular moment of the current’s charges, i.e. it will tend to conserve the angular moment.
The circulation of the charges of the continuous current in a Faraday Disc, as also in a conducting spiral, generates a continuous rate of change of angular electromagnetic moment and angular moment of matter, this works in the same way as an electrodynamic turbine. Due to the coexistence and conservation of the angular moment of the electromagnetic field and of matter, in all closed circuits there are always two equal and opposite variations of the angular moment generated.
In closed circuits, constant emf is not produced by the variation in magnetic flux, which is constant, but by two variations in the electromagnetic angular moment.
This means the new induction law will be e= -dL/dt de/dt=-df/dt in which L is the electromagnetic angular momentum and f is the magnetic flux density.
According to this new induction law, unipolar induction is a consequence and not an exception.
The generation and variation of the angular moments of the electromagnetic field and of matter, occur through the normal constraint forces acting along the path of the charges in the conductors. These constraint forces are not explicit in Maxwell’s equations. However, without these forces it would not be possible to generate or measure electric or magnetic field.
The conducting spiral allows us to see that unipolar induction is produced by a vortex of charges, confirming the Lorentz Force and invalidating Faraday’s Induction Law, furthermore it allows us to see the true origin of electromagnetic induction and its dual nature. In the conducting spiral, an inversion of cause and effect in the description of electromagnetism also becomes evident.
http://arxiv.org/ftp/physics/papers/0012/0012009.pdf
Hypercom
1. Unipolar or acyclic induction.
Possibly, there has been no simpler, more curious and polemical experiment since the beginnings of electromagnetism than Faraday’s rotating magnet and disc. For their simplicity and beauty they have always attracted the attention of the physicist.
According to Poincaré “The most curious electrodynamics experiments are those where a continuous rotation takes place, called unipolar induction experiments.”1
Einstein, in his first paper “On the electrodynamics of moving bodies,” states that: “It is known that Maxwell’s electrodynamics –as usually understood at the present time– when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena”. “Furthermore it is clear that the asymmetry mentioned in the introduction as arising when we consider the currents produced by the relative motion of a magnet and a conductor, now disappears. Moreover, questions as to the “seat” of electrodynamic electromotive forces (unipolar machines) now have no point.”2
It would seem the Faraday disc contributed to the development of the Theory of Relativity.
When studying unipolar induction back 1961, and finding the conducting spiral to be a universal unipolar generator I imagined that this must have been known since the beginnings of electromagnetism. In that year I had begun my Ph. D. course in Physics at Grenoble University and found to my surprise that the conducting spiral was unknown to my professors of electromagnetism. They suggested that I choose this for a second subject for my doctoral thesis3. It turned out to be very polemical, for as is well-known, unipolar induction continues to be the object of discussions and publications. On completing my thesis, the Board of Examiners recommended my second subject for publication; something I was only able to do years later, for in the opinion of the journal’s referee the conducting spiral was but a “mind experiment” and couldn’t possibly revolve. Only on checking the experiment (presumably), was the article accepted. This publication4 had involved considerable difficulties and scarce attention. To start with, I - the supposed discoverer - had failed to grasp the significance of the spiral. Curiously, this experiment, as straightforward and beautiful as the Faraday Disc, is just as paradoxical. Twenty-seven years after publishing my article I began my studies of unipolar induction anew with a series of experiments on conducting spirals which led me to a new understanding of electromagnetic induction, the Faraday Disc and the conducting spiral itself, establishing a new analogy between mechanics and electromagnetism. In November 1998, I attempted to publish these findings in the same journal which in 1970 had published my first article, only to have it rejected out of hand by the editor who alleged “articles announcing new theoretical results or experiments are not accepted in this journal”. Maybe he should have added: especially if they come from an unknown third-world Physicist, for this publication continues to carry articles on Faraday’s Induction Law and the Lorentz Force 5, 6, 7, 8, all of which deal with the old question as to how and where emf is generated in the Faraday Disc. Regarding the substance of the matter, some authors are of the opinion that the revolving magnet and the Faraday Disc are exceptions to Faraday’s Induction Law or flux rule9, and assure us that unipolar induction is due to the Lorentz Force, others deny any exceptions10, and still others see exceptions to the Lorentz Force11.
The difficulties in understanding the Faraday Disc derive from Faraday’s Induction Law and the equation F = il x B, which defines B and allows it to be measured. This assumes that magnetic induction B, generated by the circuit to which the segment l belongs, is negligible with regard to B. The emf and torque generated in the Faraday Disc depend on the shape of the circuit that connects the disc, giving rise to an “absolute – relative” duality of emf and Lorentz Force, which in turn, occasions different interpretations. This duality becomes much more evident in the conducting spiral and when the symmetry of the Faraday Disc is enhanced.
Some paradoxical experiments in unipolar induction which make use of the unique geometry of the spiral are described in this article. These experiments show that the paradoxes and discrepancies that arise with unipolar induction are resolved when the following analogies between mechanics and electromagnetism are established:
a) Charges, in the same way as mass, have a dual nature,
inert and gravitational, in each of these pairs neither
element is independent of the other.
b) In electromagnetic interaction among charges, both
mechanical and electromagnetic angular moments are
conserved.
c) Electromagnetic induction is due to the variation and
conservation of the angular moments of mass and
charge.
d) The possible ways of varying the electromagnetic
angular moment of a current in a circuit correspond to
the forms of electromagnetic induction.
e) The deformation of a circuit by electromagnetic forces tends to diminish the rate of change of the electromagnetic angular moment of the current’s charges, i.e. it will tend to conserve the angular moment.
The circulation of the charges of the continuous current in a Faraday Disc, as also in a conducting spiral, generates a continuous rate of change of angular electromagnetic moment and angular moment of matter, this works in the same way as an electrodynamic turbine. Due to the coexistence and conservation of the angular moment of the electromagnetic field and of matter, in all closed circuits there are always two equal and opposite variations of the angular moment generated.
In closed circuits, constant emf is not produced by the variation in magnetic flux, which is constant, but by two variations in the electromagnetic angular moment.
This means the new induction law will be e= -dL/dt de/dt=-df/dt in which L is the electromagnetic angular momentum and f is the magnetic flux density.
According to this new induction law, unipolar induction is a consequence and not an exception.
The generation and variation of the angular moments of the electromagnetic field and of matter, occur through the normal constraint forces acting along the path of the charges in the conductors. These constraint forces are not explicit in Maxwell’s equations. However, without these forces it would not be possible to generate or measure electric or magnetic field.
The conducting spiral allows us to see that unipolar induction is produced by a vortex of charges, confirming the Lorentz Force and invalidating Faraday’s Induction Law, furthermore it allows us to see the true origin of electromagnetic induction and its dual nature. In the conducting spiral, an inversion of cause and effect in the description of electromagnetism also becomes evident.
http://arxiv.org/ftp/physics/papers/0012/0012009.pdf
Hypercom