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Oct 20, 2023 at 18:53 comment added hyportnex "if the coil is moved along the field direction, no flux variation occurs and therefore no current is flowing" You are right that now $d\Phi/dt=0$, but this is not a good enough explanation for zero induced current, recall the Faraday homopolar dynamo. The difference between the two cases is that here the force and thus the free charges (electrons) would have to move parallel with the magnetic field, hence $\mathbf v\times \mathbf B = 0$, and no induced current along the wire* that is perpendicular to that motion.
Oct 20, 2023 at 17:49 history answered chewbocca CC BY-SA 4.0