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Magnetic field lines depict the strength of the magnetic field, dense lines in a region imply a strong field.

Lines are drawn as per our convenience. We needn't draw infinite lines but just relative amounts: where the field is stronger, more lines; where it isn't, less lines.

What I wanted to know was what do these lines imply when they are formed in the magnet and iron filings experiment. All this while we find that these lines can be infinite with relative spacings to depict field strength. It seems that these lines are imaginary and only for our convenience. Yet iron filings form them. So what do they imply?

Why do the iron filings follow only specific lines around the magnet? What about the spaces in between two adjacent lines? What are those spaces supposed to be? Why wouldn't the iron filings fill those up as well? Are those spaces supposed to imply absence in field?

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    $\begingroup$ possible duplicate of What are magnetic field lines? $\endgroup$ – John Rennie May 27 '14 at 8:30
  • $\begingroup$ If Iron filings would not have any breadth like an ideal line, there would not be any space. $\endgroup$ – user22180 May 27 '14 at 8:55
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The magnetic field is a continuous vector field, meaning at every point in the space you're examining you can calculate the magnitude of each component of the field (x,y,z usually). In simpler terms, every point in this space has a vector associated with it. The lines that you speak of are formed by starting at any position you choose and following these vectors. Think of it like this: you start at one of the poles of the magnets. At that point you have a magnetic field vector, essentially an arrow, you follow this arrow and arrive at a new point, with a new vector, which you then follow, etc. By doing this you'll loop back around to the other pole of the magnets. You can do this an infinite amount of times, as there are infinite points to choose from.

The iron fillings in the experiment have forces exerted on them by the magnetic field. These forces orient themselves with the vectors, so they go through te same proces I just explained. The reason there are spaces between the fillings is simply because you don't have infinite fillings, so you can't fill that space. Well, you don't need infinite fillings, but if you would fill everything up, you wouldn't be able to see the field lines because everything around the magnet would be a grey mess of iron.

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    $\begingroup$ This is not quite a complete answer. Real iron filings are aligned with the field but they are also not randomly positioned. This is because each filing gets magnetized, and attracts its neighbours. This is what causes the lines to appear. $\endgroup$ – Emilio Pisanty May 27 '14 at 15:24

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