# Magnetic field lines inside a bar magnet

Magnetic field lines are in the direction in which a North monopole would go, then inside the magnet shouldn't the magnetic field lines be towards the South Pole?

• Are there any magnetic field lines inside the magnet...? Feb 22, 2018 at 6:43

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.

No. The magnetic field lines (lines whose direction at each point along them is the direction of the magnetic flux density, $\vec{B}$, at that point) are continuous closed loops. In the case of a magnet the lines come out of the North end (not necessarily the geometrical end-face) of the magnet, curve round through the air, re-enter the magnet at the South end and go from South to North through the magnet to join up with where we started.
The lines of ${\bf B}$ are continous and unending, as in a solenoid. The lines of ${\bf H}= {\bf B}/\mu_0 - {\bf M}$ change direction at the poles a bit like the first picture in Anna V's answer. So the answer depends on what you mean by the "magnetic field lines"