... Exnihiloest is correct in stating that a voltmeter will not show a voltage if moving with the bar. However, this does not mean there is no force on the charges in the conductor ! ...
It is also what I said: "the electron doesn't see this force [F=q.VxB] because V=0 in its own frame, but instead it sees a transverse electric field which is the Lorentz transform of the magnetic field". This electric field is the source of a force F=q.E equal, in the referential of the electron, to the force F=q.VxB in the referential where the electron is seen to move at speed V. As Grumpy says: "moving the volt meter with the bar will always induce conflicting currents, which cancel out". In other words the same effect occurs both in the bar as well as in the voltmeter or ampmeter. All electrons are submitted to the same force field. If a voltmeter moving with the bar is connected to one end of the bar, its other terminal is at the same potential as the other end of the bar: current can't be seen. For a current to flow, we must loop the circuit in a reference frame from which the bar is seen to move. It is the reason why the bar has to slide relative to conductors at rest. It is the relative speed between the mobile section of the circuit and the section at rest, that creates the force imbalance onto the electrons, needed for a current. It is the same thing with gravity: a weighing machine falling with a weight can't measure the weight. We need two referential frames, the one considered at rest, and the one of the moving object. So we can recover the energy of a falling object in the referential frame where it is seen to move. Otherwise nobody can say that something moves, there is no difference between a moving referential frame and a frame at rest because nobody can say which frame is moving (1st Newton's law). We can't expect for more effects inside a so-called moving frame than in a frame at rest. There must be interactions between the "moving frame" and the "frame at rest".
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