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I am confused about the point from where magnetic field lines originate. Do they always start from the same point or are there infinitely many points from where a magnetic line originate?

If the second one is correct, then can more than one point originate from any one of those points?

I want to ask the same thing for the point where they come back to the south pole of the magnet.

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There is no particular "point of origin" in case of magnetic field lines. This is because magnetic field lines form continuous closed loops. Even inside permanent magnets (like a bar magnet), magnetic field lines join from south to north poles. Also, magnetic field lines can't intersect, which means there would be no common point from which two or more magnetic field lines could originate.

Field lines around a bar magnet

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If the $\vec{B}$ field does not vanish at a point in space (either inside or outside the magnet), then any field line through that point has to be tangent to $\vec{B}$ at that point. It is not hard to see that this implies that only one field line can pass through any point in space where the field is non-vanishing; if two field lines intersected at some point, that would imply two different directions of $\vec{B}$ at that point.

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    $\begingroup$ So the answer is no? $\endgroup$
    – Peter Mortensen
    Commented Jan 7, 2022 at 3:48
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If you believe Maxwell's equation, then $\nabla \cdot \vec{B} = 0$ says that there can be no sink or sources in a magnetic field. The field lines either form closed loops or go off to infinity.

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    $\begingroup$ There's a third option (in fact, the most common one): the field lines form a tangle of curves that fill space. IIRC there's a discussion of this phenomenon in Zangwill's Modern Electrodynamics but I don't have a my copy here at home with me. $\endgroup$
    – Michael Seifert
    Commented Jan 6, 2022 at 15:13
  • $\begingroup$ in what situations do magnetic field lines go off to infinity? $\endgroup$
    – Dodo
    Commented Jan 6, 2022 at 15:33
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    $\begingroup$ Knowing that field lines either form closed loops or go off to infinity does not tell us whether or not there is a single point somewhere through which all of the field lines pass. $\endgroup$
    – Solomon Slow
    Commented Jan 6, 2022 at 15:43
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    $\begingroup$ @Dodo : In two parallel wires having antiparallel currents, the plane of (anti-)symmetry between them contains parallel magnetic field lines arriving from infinity and proceeding to infinity. Here is a sketch of the field on a plane transverse to the current. $\endgroup$
    – Eric Towers
    Commented Jan 7, 2022 at 4:25
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    $\begingroup$ @Dodo that's "effective infinity" i.e. ouside the scale of your experiment or thought experiment. Consider a bar magnet in an intergalactic void .... $\endgroup$
    – nigel222
    Commented Jan 7, 2022 at 11:14
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There are no field lines. We draw field lines so that their density is proportional to the strength of the field around them, and we draw them in loops to capture the idea that the field is divergenceless. The drawing can communicate a pretty good picture of what the field looks like. The field around a magnet isn't zero anywhere.

Think of the contours on a topographical map. There are no contours in the real world, but we draw them so that their density is proportional to slope of the terrain around them. Field lines are similar. Don't think too much about contours, though, because the magnetic field doesn't have an analogue of height.

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  • $\begingroup$ The field lines are as real as the vector field representation. Indeed, the Aharonov–Bohm effect would focus your attention on the vector potential instead. None of these are as real as the physical field itself: they are mathematical stories we tell about the field. Which story you choose will depend on which problem you're addressing. $\endgroup$
    – John Doty
    Commented Jan 8, 2022 at 19:57
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Atoms contain atomic magnetic moment and atoms in a small region interact strongly with each other to create a small area where the field acts parallel. These are called domains which contain net magnetic moment in some particular direction.

Usually there are lots of randomly oriented domains, meaning having different directions, but when some field interacts with them (say, an external field) then they would all face to the direction of the external field, and now a net magnetic moment that is responsible for the magnetism of the magnet is created.

The reason I mentioned all this is to make clear that these domains inside a magnet must align in the same direction so as to act as a magnet. So I am saying that, as they face the same direction, the magnetic field created by each domains will add up and a net effect is created.

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    $\begingroup$ Welcome to Physics! I'm not sure this answers the question as asked; how does this relate to the geometry of the field lines that the OP is asking about? It might be good to edit your answer to clarify this. $\endgroup$
    – Michael Seifert
    Commented Jan 6, 2022 at 15:19

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