# 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?

## 1 Answer

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.

My first thought was that "magnetization" might refer to the magnetic polarization of the object, which is a vector-valued quantity that characterizes the aggregate effect of the permanent magnetic dipoles in an object. But magnetic polarization is measured in amperes per meter, not in tesla. The Wikipedia article says that real permanent magnets are often described in terms of their residual flux density, though, which is directly proportional but is measured in tesla or compatible units.

• I'm pretty sure you're right. I found out there's a paper published for this library @ sciencedirect.com/science/article/pii/S2352711020300170. In the paper itself, in section 2.1, it states "All Magpylib input and output is given in the physical units of millimeter for lengths, degree for angles, millitesla for magnetization (remanence), magnetic moment and magnetic field and Ampere for currents." So.. the magnetization vector has to be remanence. And I can convert 13200 gauss to 1320 mT. Thanks for your answer! – SomeGuy May 17 '20 at 22:50