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1b. Consider a flat conductor strip moving at speed v through a magnetic field B. A voltage will be detected across the strip at right angles to the motion, from qV X B
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In which reference frame? Not in the reference frame of the moving conductor because in that frame, V=0 and so is F=q.VxB. For this reason a voltmeter connected to the conductor and moving with it, will show no voltage.
The force is seen only by an observer in a reference frame in which the conductor moves at speed V.
2. Now, let the conductor strip be stationary and move the magnets in the opposite direction. Will there still appear a voltage V-H?
There is no voltage as well as in the first case (when we took the viewpoint of the moving conductor) and for the same reason: V=0, so F=0 whatever B.
A voltage appears only in a reference frame in which the conductor is moving. This explains why, in order to get a current in the Faraday disk, there must be a circuit in two parts: a first part at rest and a second part moving relative to the first one, in the magnetic field. The part at rest see the voltage at the terminals of the other part which is moving relative to it, and, as the two parts are connected each another through sliding contacts, a current flows.
This is basic relativity. The relative speed to be considered is not relative to the magnets whose the role is only to create the field, and a field is just a characterisation of local conditions in space to avoid to consider the sources (and consequently their speed).
Naturally if you teaches postgraduate students, one of them will surely ask: an electron flying in a magnetic field is deviated by a force F=q.VxB. An observer seing the flying electron, observes this deviation. Then how the electron, from its own referential where V=0, can feel the force and be deviated?
I guess that the answer can interest every one here, so here it is.
Relativity will once again gives the answer. The magnetic field B is the field viewed in the reference frame of the observer. We must apply the Lorentz transform of this magnetic field to obtain the field that the electron sees in its own referential. The Lorentz transform of a magnetic field gives an electric field.
In brief, the observer see a force F=q.VxB acting onto the electron moving in a magnetic field B at speed V. The electron doesn't see this force because V=0 in its own frame, but instead it sees a transversal electric field which is the Lorentz transform of the magnetic field. Naturally the two fields give the same force, it is just two points of view of the same physical phenomenon.
This topic is stimulating and reveals the power of relativity which perfectly fits the experimental observations. Pure beauty. Thanks for having evoked it. I only regret that there is no paradox that could lead us to new things...
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Topic: Relativity and Faraday's Disc Generator; Transformers and Time Delay (Read 22958 times)
