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I have been studying electromagnetic induction and I have trouble understanding some things. Say we have a square wire going through a magnetic field like in the picture (height is "h" and total length in a magnetic field is "x"). If we moved that whole conductor to the right because of the magnetic field going into the screen (j) the left-most part of the wire would experience an upwards force and therefore generate movement of electrons in that direction. That's easy enough to calculate F = q * v X B. And generated EMF is now ε = vBh.

Now if we wanted to get the same answer using flux which is Φ = ∫B * da:

Φ = B * h * x so a change in flux is Φ = Bh * dx/dt = Bh * (-v) which makes ε = Bhv, precisely what we got the first time.

My questions is: If we bring in a new magnetic field that is constant everywhere wouldn't the change in flux be 0 which would mean induced EMF is 0 but if we used the first method to calculate EMF nothing would change and EMF would still be ε = vBh.

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Might as well answer the question in case someone in the future is stuck here as well.

The change in flux is 0 but the EMF in the case of an infinite magnetic field should be 0. That's because while the force you get using Lorentz force law is indeed still there, now you have to take into account the force that the right-most wire is producing, which is in the same direction leaving you with EMS (around the loop) of 0.

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