Since magnetic field lines are the path taken by a hypothetical North Pole when it is in range of a magnetic field of a magnet, it is clear that the direction of hypothetical North Pole would be from North Pole to South Pole of a magnet not even outside the magnet but inside the magnet too, because North Pole of magnet will repel the hypothetical North Pole inside and outside the magnet and would be attracted by the South Pole of the magnet.
[Physics] Why is the direction of magnetic field from South to North Pole inside a magnet
conventionsmagnetic fieldsVector Fields
Related Solutions
I was puzzled, like you , because I expect that if there exist magnetic monopoles, due to the symmetry of the maxwell equations the dipole should be analogous to the electric dipole. I just found this in my searches.
There are two models of magnetic dipoles , one assuming that two north and south poles could exist independently, the other using the solenoid model.
Notice that, in the external region away from the charges or current loops, the field lines for the two models point in the same directions, but in the internal regions (in between the charges of the Coulombic dipole, and inside the current loop of the Amperean “dipole”) the field lines point in opposite directions.
These two models, which might be called Coulombic and Amperean dipoles respectively, are illustrated (crudely)
.....
Determining the field surrounding a (hypothetical) Coulombic dipole model is fairly straight-forward, patterned after the usual treatment of electric dipoles (see, for example, Becker’s “Electromagnetic Fields and Interactions”).
There are references to the statements and if interested you should read the link.
My handwaving argument (too rusty to chase the mathematics) is that if we had magnetic monopoles, there would be symmetric solenoid type solutions for magnetic currents ( with magnetic monopoles ) that would produce an electric dipole, different from the coulombic electric dipole, just from the symmetry of the equations.
As there is no indication that magnetic dipoles exist, I tend to accept that the solenoid model, with closed magnetic lines, is the one to use, so inside a magnet the lines go from south to north in order to close. Your "the direction in which a north monopole would go " belongs to the coulombic model.
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
Best Answer
In nature, there is no magnetic monopole discovered yet. All of the magnets we have are created by certain kind of current (like the spin of an electron). Thus, the prototype of a magnet is a solenoid.
Now, there are a bunch of ways to argue the direction of the magnetic field in the solenoid. If you took introductory physics before, please use Biot-Savart. If not, the most intuitive way is probably assuming that magnetic field should be smooth (this is based on the assumption of no magnetic monopole). The north pole is defined as where the magnetic field comes out. Due to the smoothness assumption, even when you go into the solenoid a little bit (from north pole), the direction of the magnetic field should be the same, which is now "pointing toward north pole". Thus, it should be pointing from south pole to north pole inside.