Faraday’s Law

1. The problem statement, all variables and given/known data
So this is more conceptual than anything. Say there is a wire loop on the x,y axis and a permanent bar magnet above it on the z axis. I understand according to Faraday’s law that as the north end of the bar magnet moves towards the loop the magnetic flux is increasing. Conversely, if the magnet was flipped and the south end was pointing down towards the wire loop, as the magnet moved closer would magnetic flux decrease?

As I understand it, with electric flux and gaussian surfaces electric field lines going in was increasing flux and out was decreasing flux. So, does this happen for bar magnets? Since the magnetic field lines make loops from north to south, technically moving it closer would result in more field lines pointing in going through making the flux negative? Or does it not matter and the magnetic flux is always positive?

As an aside: when one has a wire loop on the x,y axis and a bar magnet above it on the z axis with its north end pointing into the loop. As you move it in the wire loop and through it does the magnetic flux peak when the magnet’s center is in the center of the loop then decrease back to 0 or does it jump negative as soon as it makes it over half way?

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