I learnt Faraday's Law of Induction however I was confused about why the area aspect of magnetic flux impacts on the EMF generated.
Why do magnetic field lines inside the coil area affect the EMF generation? I was taught that the reasoning behind Faraday's Law was that the relative motion between the magnetic field lines and the coil invoked the Lorentz force on the electrons, pushing them into a current. So why should the magnetic flux through the center of the coil do anything? Only the magnetic flux change AT the wire itself should be inducing current right?
So I thought of the experiment below. In the diagram below (sorry it's so poor quality), the black circle is a solid loop of copper wire and the red X's are solenoids. If I turn on the solenoids, shouldn't I get an EMF of equal magnitude compared as if I put the coil into a bigger but equal magnitude magnetic field?