Question (by Supratech) for a senior lecturer giving lectures in electrodynamics at a Teachers' College: What is your opinion of the physical possibilities of shielding a part of PHG circuit by a superconductor?
Reply (Professor): The superconductor forces the magnetic field out of its volume. This field disturbs the external magnetic field. If it is rotationally symmetrical, then this symmetry is disturbed and the field becomes more heterogeneous. If any voltage is induced, then the superconductor does not influence the current flowing through the circuit. Another physical interpretation: With respect to the orientation of the shielded leg along the axis parallel with the flux lines, the induced voltage would not be generated in case of a homogeneous field as the magnetic force exerted on electrons would be null even without shielding. In case of small dispersion of the magnetic flux lines, nevertheless, it could actually induce such voltage. In my opinion, the superconducting shield is not of any significance.
Response (Supratech): The measurement shown in Figure 3 in version 2 of report https://arxiv.org/abs/1601.07750v2 shows that the course of the resulting induction component B is not by far parallel with the PHG body. If this was the case, then the resulting perpendicular component (i.e. the component actually influencing the conductor) would be null and the relationship divB = 0 could not be preserved, resulting in an immediate conflict with the theory. PHG would be functional even without modifications with shielding.
The superconductor forces the field out of its volume. The flux lines always flow around the superconducting shield along the shortest path. There is practically no component of the flux lines parallel with the shield. It is therefore circumfluenced by the perpendicular components, which flow along the shortest paths possible. The circumfluencing flux lines cannot have any influence on the circuit, which is out of the shield scope. In version 3 of report http://www.supratech.org/cz/public/indukce.pdf, the shield is situated differently but with the same result.
Question (Supratech): What is your opinion of the existence of EMF imbalance (electromotive force) when a superconducting shield is used in PHG?
Reply (Professor): With reference to the previous case, I should say that magnetic shielding would only be meaningful in case of a heterogeneous field but its influence would not be essential due to the fact that the conductor would be oriented in parallel with the ideal flux lines. The imbalance of electromotive forces is caused by another flow of magnetic induction through legs i and i´
Response (Supratech): In version 3 of the report, the shield is situated differently but with the same result. The paths of the flux lines along the FHG body is hypothetical only. Again, I would like to make a reference to Figure 3 in version 2 of the report. In your terms of imbalance in the mentioned legs, PHG would be functional even without any shielding.
Question (Supratech): Is the result of the experiment with shielded PHG expectable or not, or is it new in any way? If not, we would appreciate some explaining references etc.
Reply (Professor): If, in case of stationary rectangle coil, it is only the magnets which are in motion, then we can assume that the magnetic flux lines (magnetic field) can enter the coil area due to its heterogeneity, which is caused by the magnetic flux lines emerging from the neodymium magnets in the lower part. Another contribution to this may come from the field, which is shielded, i.e. Forced out of the volume of the shielding superconductors. This means that we assume asymmetrical magnetic field, which is variable in time due to the coaxial rotation of the magnets and to the magnetic flux lines entering the coil area; this would also partially modify the magnetic induction flux.
If it is the coil which is rotating, then the condition for emergence of induced voltage is met by the fact that the coil “intersects” the magnetic field by its leg i and i´. As shown in Figure 1, there is a rectangular area in the lower part; in our case, its shape would be circular. However, we need to discuss the heterogeneity of the field in the layout of the disc magnets. Homogeneity can be expected in the lower part (depending on the distance from the lower magnet) and on the side with the superconducting shield as these are the places where the field is shielded. The field does not reach the leg j but contributes to the heterogeneity of the overall magnetic field. Electrical induction can occur in the upper and lower parts i and i´ but cannot emerge in part j due to the shielding; it also cannot be seen along the axis passing through the conductor in parallel with the flux lines (i.e. in case of homogeneous field).
Response (Supratech): As I said in the previous answer, the field does not show such idealized distribution. Since there is no universal reference system, it makes no sense to assess the induction situation with respect to stationary magnets or stationary coil. Both aspects are identical and their physical results are also the same.
Question (Supratech): How would you explain the Faraday's paradox?
Reply (Professor): My explanation of the Faraday's paradox in case of conventional homopolar brush generators, i.e. of the fact that there is not induction inside the stationary disc, consists in the statement that the magnetic field is constant even when the magnets are rotating so no magnetic flux can occur. This also applies to any deformation of the field due to superconducting shield. (As you pointed out correctly, the condition divB = 0 is still met). On the other hand, if the disc rotates with respect to the magnetic field, then it is the electrons in the conductor which are in motion, and this flow of electron generates a magnetic field, resulting in induction in the brushes.
In the case of a brushless motor of your design, the conductor (frame) is stationary and there is no induction. That is why you cannot measure any value.
Response (Supratech): I can say definitely that it does not matter at all which reference you use for assessment of PHG/FHG function. Both systems are equivalent. I should, however, point out that the existence of a privileged inertial system - ether - has been gradually infirmed by the Michelson&Morley’s experiment and disproven by the relativity postulates since 1905. If we recognize the relativistic explanation of the Faraday's paradox, we find out that there is actually no paradox: It does not matter whether the disc is rotating and the magnet is stationary or it is the other way round. Both cases are characterized by EMG induction balance. The external and internal contributions of EMF are equal due to the basic condition divB = 0. This implies a zero induction, applying also to unshielded PHG. In FHG, though, there is an induction imbalance of EMF due to the fact that the disc is fixed to the magnets. This means that the internal flux does not contribute to the generation of EMF. The external flux lines are in motion with respect to the frame with brushes and, as such, should induce EMF from the external flux.
Note (Supratech): We would like to thank you, Professor. We are well aware that the problem of FHG has not been explored in full so far and there is a lack of knowledge in this area namely in Teachers' College. The interview has been edited for the sake of maximum conciseness and better understanding of the subject matter of the dispute. We have also encountered similar naive explanation of the function of FHG in certain researchers at CTU Prague. Examples of such non-complex explanation is available at http://worldnpa.org/abstracts/abstracts_5875.pdf or https://en.wikipedia.org/wiki/Homopolar_generator .
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