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Electromagnetic induction

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Hello everyone,

One very basic thing about this phenomenon is not very clear to me. If a conductor moves in a region of uniform magnetic field, would it have an EMF induced across it? I'm confused because as per Faraday's law, a change in flux through the conductor is necessary for EMF to be induced in it but if the flux is everywhere the same in the region where the conductor is moving, there should be no change in flux through it and consequently, no EMF in it.

How much wrong am I?

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