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Okay so this is a pretty famous statement made to anyone who is introduced to the magnetic effects of electric current a.k.a. electromagnetism:

The relative strength of the magnetic field is shown by the degree of closeness of the field lines.

But it never made sense to me so I dropped the idea of studying e.m. deeply and just overviewed it superficially and somehow managed to pass the exam and moved to the next class. It's not until recently that I realised that we have the same chapter again in highschool graduation so I thought I'd better ask.

Yeah so we were told that field lines arise from north pole of a magnet and are closed curves going "into" the south pole (and run parallel to each other inside the magnet?) Then there's that statement. Out teacher drew small equal-area boxes showing that the one's "near" the poles contain in themselves more field lines than the ones farther apart(ring a bell?). But isn't it like every point in space has a field line passing through it? I mean there is exactly just as much "space" (or 2 dimensionally, area) in the other box as is in the first one. There can't be regions having no magnetic field in-between those lines? Isn't it kinda wrong?

My old textbook?

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  • $\begingroup$ Minor comment to the post (v2): Please consider to mention explicitly author, title, etc. of link, so it is possible to reconstruct link in case of link rot. $\endgroup$ – Qmechanic May 6 at 10:15
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The question you have asked is valid and is basically about nature of field lines. Now, I would explain using electric field lines ( not magnetic field lines about which you asked ) because the idea is easier to grasp using electric field lines emanating from a charged particle and is similar to magnetic field lines.

So, consider a positive charge located somewhere in space. Obviously, field lines will emanate radially out of the charge because positive charges would feel repulsion against the charge. To show this, although you know that field lines are present everywhere, you will chose a fixed number of uniformly spaced lines showing the direction of electric field.

You will see that these lines look like spikes of a bicycle, and you would notice that number of field lines per unit volume is more when near the charge and decreases as we go away. You should note that in reality electric field is present everywhere in space and what happens is that it gets weaker as we go away from the charge. We can see that we get a very good picture which shows the relation between electric field strength and density of field lines. More the density of field lines, more is the strength of the field.

The above is the general idea behind using field lines, as it gives both the direction and strength of the field. You can always chose to increase the number of field lines, and it is the relative density which counts.

I hope this answers your question.

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