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Lenz's law states that the direction of the induced electromotive force (emf) in a circuit is such that it opposes the change in magnetic flux that produced it.
When a metallic rod held horizontally along the east-west direction is allowed to fall under gravity, it will experience a change in magnetic flux if there is a magnetic field present in the vicinity of the rod. However, for the scenario described, assuming there is no external magnetic field, there will be no change in magnetic flux experienced by the rod as it falls.
Since there is no change in magnetic flux, according to Faraday's law of electromagnetic induction, there will be no induced electromotive force (emf) generated in the rod. Faraday's law states that the emf induced in a circuit is directly proportional to the rate of change of magnetic flux through the circuit. If there is no change in magnetic flux, there will be no induced emf.
Therefore, in this scenario, as the metallic rod falls under gravity along the east-west direction without encountering any external magnetic field, there will be no emf induced at its ends.
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