Magnetic Flux: Does Direction Matter?

[physicsrequire]

Homework Statement

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 magnetic flux? 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 when moving towards the loop?

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?

 

[BvU]

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?

Conceptual is important. Sometimes a lot more important than getting the right answer for anything .
Flux is a scalar, but it has a lot has to do with direction. In the definition you have an inner product between the magnetic field vector and the surface normal. Flip $\vec B$ and you get the opposite sign for $\Phi$.

with electric flux and gaussian surfaces electric field lines going in was increasing flux and out was decreasing flux

rephrased: with a gaussian surface that has the surface normal pointing (outward or inward, either way - depends on the orientation and determines the direction of the contour!), electric field lines going in the direction of the surface normal make a positive contribution to the flux and electric field lines going opposite to the direction of the surface normal make a negative contribution to the flux. The electric flux is an integral, just like in the magnetic case.

The aside gives me a headache. Instead of aspirin, I use google "magnet falling through a coil" and come up with e.g. this and this (even better). Conclusion: peaks (time derivative is 0, goes from + to -). Makes sense: all the magnetic field lines that go from N to S outside the magnet over the rest of the space are returning from S to N densely packed inside the magnet ! Make a drawing (I needed to !)