Magnetic Flux: Does Direction Matter?

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In summary, the conversation discusses the relationship between a wire loop on the x,y axis and a permanent bar magnet above it on the z axis. It is stated that according to Faraday's law, as the north end of the magnet moves towards the loop, the magnetic flux increases. The question is then posed whether the magnetic flux would decrease if the magnet was flipped and the south end was pointing towards the loop. It is then explained that the electric flux and gaussian surfaces have a similar relationship, with electric field lines going in or out contributing positively or negatively to the flux. The conversation also briefly mentions an aside about the behavior of magnetic flux when a magnet is moved through a wire loop.
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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?

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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 !)

What is magnetic flux?

Magnetic flux is a measure of the amount of magnetic field passing through a given area. It is represented by the symbol Φ and is measured in units of webers (Wb).

What is the direction of magnetic flux?

The direction of magnetic flux is determined by the direction of the magnetic field lines passing through the given area. This direction is typically represented by an arrow pointing in the direction of the field line.

Does the direction of magnetic flux matter?

Yes, the direction of magnetic flux is important as it determines the direction of the magnetic force acting on a charged particle moving through the given area. It also affects the direction of induced currents in conductors.

Can magnetic flux change direction?

Magnetic flux can change direction if the direction of the magnetic field or the orientation of the area through which the flux passes changes. This can happen due to the movement of a magnet or changes in the shape or position of a conductor.

How is magnetic flux calculated?

Magnetic flux is calculated by multiplying the strength of the magnetic field (B) by the perpendicular area (A) through which the field passes. This can be represented by the equation Φ = B x A. The direction of the magnetic field and area must be taken into account when using this equation.

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