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My physics textbook defines the direction of the magnetic field as the direction of the force on a small north pole of a magnet. However, I am told also that if you have, say a bar magnet, that the north pole has a field coming out of it and curving towards the south pole. But we are also told that it then continues back and returns to the north pole, why? It doesn't make sense, does it, that a small north pole of a tiny magnet would go back from the south pole to the north pole, which it is repelled from!

Here's an icon of that sort from the internet.

A bar magnet with the magnetic field going through the loop

Image from http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html

See the curve of the electromagnetic field, why does it come to the southern pole and then heads back to the north pole? What causes a tiny north pole to want to go back north?

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First, there is no such thing in real life as an isolated North or South pole. This implies that magnetic field lines always form closed loops, as you see in the image. This is codified in Gauss's Law of Magnetism.

Your textbook, while I can sort of see the logic, gives a very inelegant definition for field lines. Don't think of the field lines as a force on a tiny test bar magnet that will push it. Think of it as forcing the tiny magnet to orient a certain way. If you had a compass (which is precisely a tiny magnet), and put yourself as a tiny person into your diagram and started walking around, your compass would always point in the direction of the local field line, including if you were inside the bar magnet. Hope that is helpful

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  • $\begingroup$ I grant that there isn't an isolated north or south monopole. But supposing that the tiny test bar magnet is placed inside the other magnet, why would it orient itself so that the northern points to the northern, shouldn't it orient itself so its northern pole now points to the southern pole of the bar magnet in question? $\endgroup$ Commented Sep 17, 2021 at 5:46
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    $\begingroup$ No, the tiny magnet would align itself to the large magnet's field. Don't think of the rule of magnets as " opposite poles wanting to attract." That's only true in certain cases. It's about the field lines wanting to align. $\endgroup$
    – RC_23
    Commented Sep 17, 2021 at 16:03
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The thing to remember is that there is no such thing as a tiny "north" magnet since every magnet contains a north and south pole no matter how small it is.

Magnetic field lines always form closed loops and this is a statement of the fact that the are no magnetic monopoles (that have been observed) no matter how tiny the magnet is, or in other words, every magnet has a north and south but never just a north or south on their own.

This is mathematically stated in the Maxwell equation $$\nabla\cdot {\bf B}=0$$ That is, the magnetic field never diverges.

The reason why the concept of a test "north magnet" is used in these cases, is that if you placed it in the magnetic field of the larger one (at the north pole), it will move away from the north pole along toward the south pole of the larger magnet, along the lines of force, as shown in the diagram.

In reality, this will not happen since no such "north magnet" exists, and this example is used to illustrate the direction of the lines of force of a magnetic field. The important thing to remember is that all magnets have two poles, regardless of their size.

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  • $\begingroup$ Simply to complete the previous explanations: magnetic field lines do not generally form closed curves. The "proof" of this result is never given. They only form closed curves in a few very symmetrical cases. $\endgroup$ Commented Sep 17, 2021 at 6:30
  • $\begingroup$ Are you saying there are magnetic monopoles or that magnetic field lines neither start nor end? Or there is no actual proof that magnetic monopoles do not exist? What are you saying? $\endgroup$
    – joseph h
    Commented Sep 17, 2021 at 6:39
  • $\begingroup$ Yes : more often, magnetic field lines neither start nor end. This does not pose a problem for a curve which can remain in a bounded domain without being closed. This is also the case for the trajectories of the planets in a field which is not strictly central. $\endgroup$ Commented Sep 17, 2021 at 6:43

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