# What is a magnetization vector, and how can it be computed?

So I know that this is a physics related site, but I'm trying to use a Python library called magpylib to compute magnetic flux at various positions from a joystick magnet. The documentation includes an example of how it can be used.

You'll notice that there's this concept of a "magnetization vector" that describes the magnet. What is a magnetization vector? I was thinking the magnetization vector is probably something describing the strength of a magnet. I thought maybe it would have been a sum of all the vectors in the vector field of the north half of the magnet.

But then I looked at the source code and a comment describes it as "Magnetization vector of magnet in units of [mT]." This confuses me as mT is a unit of flux. Isn't flux basically a count of the number of magnetic field lines going through a surface? In that case, is magnetization vector describing how many magnetic field lines are coming out of the surface of the magnet at the north pole?

What exactly is a magnetization vector? And also, let's say I know the following about the magnet:

• Brmax: Residual Induction / Residual Flux Density / The magnetic induction remaining in a saturated magnetic material after the magnetizing field has been removed: $$13200\ \text{Gauss}$$

• BHmax: Maximum Energy Product / The Maximum Energy Product at the point on the B/H Curve that has the most strength, expressed in $$\mathrm{MGOe}$$ (MegaGaussOersteds): $$42\ \mathrm{MGOe}$$

• magnet dimensions: ring magnet with 1/4 inch outer diameter, 1/8" inner diameter, x 1/16" thick

With this information, is it possible to go and compute the magnetization vector? Or is more information needed?

The documentation for the package doesn't seem to identify a formula that would make it unambiguously clear what they mean (maybe it could be found by checking the source). But knowing that it's measured in $$\mathrm{mT}$$, or millitesla (which is actually a unit of magnetic flux density, not flux), my best guess is that it refers to the residual flux density (or remanence) of the magnetic object.