Why does the given diagram not violate Gauss's law of magnetism?

[phosgene]

Homework Statement

I'm basically just wondering why the given diagram wouldn't violate Gauss's law of magnetism...there are two B-field lines exiting, but none entering the red box. So the net flux isn't zero. I vaguely remember the lecturer addressing this when we were studying the topic, but this was wwaaay back in first semester and I've forgotten. And I can't find the answer in the textbook.

Homework Equations

$\oint{B \bullet dS}= 0$

The Attempt at a Solution

EDIT: I DO remember a bit now, he said that the magnet is actually composed of lots of little N-S parts, but then what if the red box slices through the middle of one of those?

 

[aralbrec]

wondering why the given diagram wouldn't violate Gauss's law of magnetism...there are two B-field lines exiting, but none entering the red box.
EDIT: I DO remember a bit now, he said that the magnet is actually composed of lots of little N-S parts, but then what if the red box slices through the middle of one of those?

Yes, there is flux entering on the left side of the box from the magnet. Connect the flux lines from S through the magnet to the N. Those lines you have drawn are loops that do not simply terminate on the magnet poles.

EDIT: I DO remember a bit now, he said that the magnet is actually composed of lots of little N-S parts, but then what if the red box slices through the middle of one of those?

The magnetism in permanent magnets is caused by the movement of some electrons around individual atoms.

You should recall that a loop of current generates a magnetic field (it was likely called a magnetic dipole). An electron orbiting its nucleus also constitutes a loop of current, as does an electron spinning on its own axis. Normally electrons are paired in orbits so their net magnetic contribution is zero (one generates NS and the other SN so they cancel) but the orbitals of some materials are modified when atoms come close together (like in a solid) so that they are no longer paired and that is what leads to some materials being magnetic.

Each atom with an orbiting electron generating a magnetic field can be considered a magnetic dipole with an N and S and that is why it is said a permanent magnet can be thought of as having many tiny N/S poles. It's also why you can never cut a permanent magnet in half and isolate the S from the N.

A distinction between macroscopic and microscopic properties also has to be made. In the sort of diagram above, we are looking at the macroscopic properties of the magnetic field, which averages the effects of all the individual atoms of a material. If you zoom into the atomic scale, irregularities in the lattice (the way atoms are bonded to each other; there can be an atom missing here, an extra one there; different areas of the molten material may have crystallized separately so where individuals islands of crystals meet is not a regular lattice bond, etc) can cause large local fluctuations in the magnetic field. Don't worry about that though, just worry about the macroscopic scale because that's what we're mainly interested in.

 

[phosgene]

So, if I've understood correctly, magnets essentially boil down to collections of something like this:

where the red represents the movement of the electron and the black lines are B-field lines. If that is the case, I think I can see why the net flux through a closed surface is always 0. Thanks :)

 

[Delphi51]

You've got it!
There are NO magnetic monopoles except in Larry Niven science fiction stories.