Magnetic flux through a closed surface

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Magnetic flux through a closed surface is always zero, even if the surface encompasses one pole of a magnet, because the magnetic field lines entering and exiting the surface cancel each other out. This is supported by Maxwell's Equations, specifically that the divergence of the magnetic field (Div(B)) is zero. The discussion highlights a common misconception among newcomers to electromagnetism, particularly regarding the behavior of magnetic field lines. Both the North and South poles of a magnet have field lines entering and exiting, which leads to confusion about their distinction. Understanding that magnetic field lines are continuous and loop back through the magnet clarifies the nature of magnetic poles.
tomwilliam
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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
 
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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.
 
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?
 

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