Question about Flux through a closed surface

[Hoserman117]

I understand that magnetic flux through a closed surface is zero, but what is the exact definition of a closed surface? The textbook I'm using is rather vague with this definition and I want to make sure I have the definition nailed down for the exam in case my professor tries anything tricky.

 

[Hoserman117]

I think I may have just answered my own question. I think I've been reading over everything too quickly and not paying attention to the difference between flux and net flux.

Either way, some clarification could be nice. Would a flat disc still be considered a closed surface, with a net flux of zero, but applying flux=BAcos(theta) still give the flux out of the surface?

 

[jtbell]

what is the exact definition of a closed surface?

Here's my attempt at a loose definition:

A closed surface has no "edge". So long as you stay on the surface, you can go round and round forever without running into any "edge" that stops you. An open surface does have an "edge" and you eventually encounter it so that you can proceed no further.

For anything better that that, you'll have to appeal to the mathematical branch called "topology."

A flat disc is not a closed surface, because (under my definition) sooner or later you reach its edge.

A spherical surface, on the other hand, is closed because you can go round and round on it forever; and this doesn't change if you distort it into another shape, so long as you don't "tear" it so as to introduce new "edges."

 

[tomwilliam]

Can you set up a closed surface around one of the poles of a magnet? The problem I have is that it seems to violate the principle that the magnetic flux through a closed surface is always zero. Thanks

 

[jtbell]

Can you set up a closed surface around one of the poles of a magnet?

Sure, provided we let the surface pass through the magnet.

The problem I have is that it seems to violate the principle that the magnetic flux through a closed surface is always zero.

It doesn't. Consider the bar-magnet field lines in the diagrams on this page:

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html

Note the direction of the field lines inside the magnet.

 

[tomwilliam]

Thanks.
So is it fair to say that if you create a closed surface around a single pole of a magnet, you still have field lines coming in and going out...meaning that the single pole is actually a dipole? In that case, I'm wondering whether splitting a magnet up into two poles is actually feasible, theoretically. I know that if you cut it in half, you create two dipoles...but if they actually remain as one it seems that each pole contains a dipole...if you get what I mean.
I realize that is a bit garbled, but hopefully someone will understand the question!