Transformation of Fields, Assuming Galilean Transformations
Assuming that the magnet frame and the conductor frame are related by a Galilean transformation, it is straightforward to compute the fields and forces in both frames. This will demonstrate that the induced current is indeed the same in both frames. As a byproduct, this argument will also yield a general formula for the electric and magnetic fields in one frame in terms of the fields in another frame.
In reality, the frames are not related by a Galilean transformation, but by a Lorentz transformation. Nevertheless, it will be a Galilean transformation to a very good approximation, at velocities much less than the speed of light.
Unprimed quantities correspond to the rest frame of the magnet, while primed quantities correspond to the rest frame of the conductor. Let v be the velocity of the conductor, as seen from the magnet frame.
Read more about this topic: Moving Magnet And Conductor Problem
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