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In the picture below, the rectangular coil of wire is moving out of the page, so that only its upper part lies within the magnetic field.

This movement creates motional emf in the upper side of the coil, and current is supposed to flow.

However, there is no change in flux through the coil, so by Faraday's law, there should be no emf.

Where did I go wrong?

Thank you.

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  • $\begingroup$ Are you 100% sure that you have interpreted the problem right? Your sketch is not clear as well... $\endgroup$
    – basics
    Commented Sep 12, 2022 at 17:16
  • $\begingroup$ I assumed that the upward red arrows were supposed to denote an 'upward' magnetic field through all space in and around the rectangle. In this case you would get (equal) motional emfs in the top and bottom and bottom sides, but one would be clockwise and the other anticlockwise. $\endgroup$
    – Philip Wood
    Commented Sep 12, 2022 at 18:02
  • $\begingroup$ I guess so as well, and this will be one of the most classical set-up in Electromagnetism. If it is so, I'm pretty sure that @Matan E. didn't understand the problem $\endgroup$
    – basics
    Commented Sep 12, 2022 at 18:45
  • $\begingroup$ This is not a problem from a book $\endgroup$
    – Matan E.
    Commented Sep 13, 2022 at 4:47

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You assume unphysical magnetic field (magnetic field violating the condition of zero divergence, sometimes called the Gauss law of magnetism).

You can see this by figuring out magnetic flux through a closed surface of a cuboid set up around the red horizontal line. Flux on the top-side face is non-zero, flux on all other faces is zero. That is not possible for magnetic field.

Realistic magnetic field will be non-zero almost everywhere in the circuit. If the flux through the circuit is zero, net motional emf in the circuit will be zero.

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