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The problem is posed as follows:

There is a conductor and a magnet in relative motion. This motion induces emf in the conductor. The value of the induced emf is independent of whether it's the conductor or the magnet that is moving.

This phenomenon has two different explanations depending on the frame of reference one is in. If one is in a frame at rest with respect to the conductor and the magnet is moving, the induced emf results from the variation in the magnetic flux which produces electric filed as dictated by Faraday's law.

On the other hand, if one is in a frame that is at rest with respect to the magnet and the conductor is moving, then the induced emf is a result of the lorentz force acting on the charge carries moving in a magnetic field.

This problem was one of the motivations that led Einstein to develop SR:

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. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. For if the magnet is in motion and the conductor at rest, there arises in the neighborhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighborhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise – assuming equality of relative motion in the two cases discussed – to electric currents of the same path and intensity as those produced by the electric forces in the former case.

So yeah, We have physical situation that depends only on the relative motion, But the laws of physics draw a distinction between what is moving and what is at rest.

But I still can not understand what is problematic about this situation?

What is wrong about using two different laws of physics(Lorentz force and Faraday's) depending on one's frame of reference to describe the same phenomenon?

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  • $\begingroup$ One need a deeper understanding of what are Lorentz force, electric and magnetic induction. How they are related you can read in my elaboration "About the internal cause of Lorentz force, electric and magnetic induction" $\endgroup$ – HolgerFiedler Oct 17 '15 at 15:28
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    $\begingroup$ I think it has to do with which field causes the current to flow in the conductor. Before relativity, the electric and magnetic fields were seen as two separate fields. In the first case, the movement of the magnet induces an electric field, the force due to which induces the current. In the second case, the magnetic Lorentz force makes the charges move, thus inducing a current. This distinction, I suppose, is what led Einstein to develop the "electrodynamic" picture we all know so well. $\endgroup$ – Prish Chakraborty Oct 17 '15 at 16:55
  • $\begingroup$ I'd rather go along the lines of @PrishChakraborty: whatever were the original motivations of Einstein, he establishes the rules of the change of the frame of reference of the electromagnetic field object $F$, not the separate electric and magnetic fields. There are a lot of polemics about the original motivations, especially because the moving magnet paradox is seen already at velocities far below the relativistic corrections ... but this is just an illustration, and Einstein's proposal for the space-time and electromagnetism transformations is mathematically correct, though beyond intuition. $\endgroup$ – FraSchelle Oct 21 '15 at 8:00
  • $\begingroup$ @PrishChakraborty Actually, Ampère coined the word "electrodynamic." $\endgroup$ – Geremia Jun 24 '16 at 4:30
  • $\begingroup$ @Geremia : Einstein developed relativistic electrodynamics, which is what I was referring to. $\endgroup$ – Prish Chakraborty Jun 24 '16 at 5:03
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Nothing is problematic with it.

As FraSchelle says above—and is also true in the development of many other physics theories, in that they are, over time, purified of the scaffolding that helped construct them*—the original motivation doesn't affect the content of the developed theory.

*cf. the top of p. 90 (PDF p. 91) of Stefano Bordoni's When Historiography met Epistemology: Pierre Duhem's early philosophy of science in context for some historical examples

Einstein, when discussing the "asymmetries which do not appear to be inherent in the phenomena," was referring to a particular interpretation of Lorentz's electrodynamics that he learned, during 1896-1900, from an 1894 book by Föppl.

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