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I have a metallic rod which is being rotated in a constant magnetic field. The EMF is produced in it as per motional EMF and can explained using the Lorentz force. But how can we explain the production of EMF in it using Faraday's flux rule. In this case the rod is in constant magnetic field and even though rod is rotating, the flux is not changing. So as per Faraday's law, there shouldn't be any EMF.

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  • $\begingroup$ I don't have time to write a good answer at the moment but peruse the following Wikipedia article, Faraday paradox, and note that the rate of change of magnetic flux through a surface involves two terms when the contour of integration is changing with time. $\endgroup$ Oct 31, 2017 at 15:31
  • $\begingroup$ The have an EMF you need to have a closed loop. The two ends of the rod are at different points, and if you connect them to a voltmeter, the reading on the meter will depend on where the leads connecting the ends are, and how they are moving. $\endgroup$
    – mike stone
    Jul 12, 2021 at 15:51

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... how can we explain the production of EMF in it using Faraday's flux rule? In this case the rod is in constant magnetic field and even though rod is rotating, the flux is not changing.

Faraday’s law is derived from the observation of changing electric or magnetic fields like in transformers.

The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux enclosed by the circuit. (Wikipedia

More general there are three cases of the involved components:

  1. Lorentz force / electric device: An electric current in a magnetic field give a deflection of the wire (of the electrons in this wire).
  2. Electric generator: The movement of a wire in a magnetic field (of course not parallel to the magnetic field) induces a current in the wire.
  3. Electromagnet: A current in a coil induces a magnetic field.
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