Why is magnetic flux zero through a closed surface containing one pole?

[tomwilliam]

This is always zero, right?

What if you construct a closed surface which only encompasses one of the poles of a magnet? Surely there would then be a non-zero flux as the inside of the surface would constitute a source (or sink) of magnetic field lines.

I'm new to electromagnetism, so any help appreciated.
Tom

 

[Foofur]

Nope. What makes you think it would have a nonzero net flux? Just imagine what the setup looks like and you'll see that the flux will cancel.

Alternately just look at the Maxwell Equations (assuming that you believe in them of course). Div(B)=0.

 

[tomwilliam]

Thanks. I had forgotten that the magnetic field lines can be thought of as passing through the inside of the magnet, so I take your point that they all cancel out.

That brings up a new question though: if the North pole of a magnet has field lines coming in and going out of it, and so does the South pole, then what exactly distinguishes them. As you can imagine, I've been approaching this as if it were electrostatics (hence not realising that the field lines pass through the centre) but it strikes me that there doesn't seem to be a difference between the two poles of the magnet...am I barking up the wrong tree?