# Magnetization

In classical electromagnetism, magnetization or magnetic polarization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. The origin of the magnetic moments responsible for magnetization can be either microscopic electric currents resulting from the motion of electrons in atoms, or the spin of the electrons or the nuclei. Net magnetization results from the response of a material to an external magnetic field, together with any unbalanced magnetic dipole moments that may be inherent in the material itself; for example, in ferromagnets. Magnetization is not always uniform within a body, but rather varies between different points. Magnetization also describes how a material responds to an applied magnetic field as well as the way the material changes the magnetic field, and can be used to calculate the forces that result from those interactions. It can be compared to electric polarization, which is the measure of the corresponding response of a material to an electric field in electrostatics. Physicists and engineers usually define magnetization as the quantity of magnetic moment per unit volume.[1]It is represented by a pseudovector M.

## Definition

The magnetization field or M-field can be defined according to the following equation:

${\displaystyle \mathbf {M} ={\frac {d\mathbf {m} }{dV}}}$

Where dm is the elementary magnetic moment and dV is the volume element; in other words, the M-field is the distribution of magnetic moments in the region or manifold concerned. This is better illustrated through the following relation:

${\displaystyle \mathbf {m} =\iiint \mathbf {M} \,dV}$

where m is an ordinary magnetic moment and the triple integral denotes integration over a volume. This makes the M-field completely analogous to the electric polarisation field, or P-field, used to determine the electric dipole moment p generated by a similar region or manifold with such a polarization:

${\displaystyle \mathbf {P} ={d\mathbf {p} \over dV},\quad \mathbf {p} =\iiint \mathbf {P} \,dV}$

Where dp is the elementary electric dipole moment.

Those definitions of P and M as a "moments per unit volume" are widely adopted, though in some cases they can lead to ambiguities and paradoxes.[1]

The M-field is measured in amperes per meter (A/m) in SI units.[2]

### Physics application

The magnetization is often not listed as a material parameter for commercially available ferromagnets. Instead the parameter that is listed is residual flux density, denoted ${\displaystyle \scriptstyle \mathbf {B} _{r}}$. Physicists often need the magnetization to calculate the moment of a ferromagnet. To calculate the dipole moment m (A⋅m2) using the formula:

${\displaystyle \mathbf {m} \;=\;\mathbf {M} V}$,

we have that

${\displaystyle \mathbf {M} ={\frac {1}{\mu _{0}}}\mathbf {B} _{r}}$,

thus

${\displaystyle \mathbf {m} ={\frac {1}{\mu _{0}}}\mathbf {B} _{r}V}$,

where:

• ${\displaystyle \scriptstyle \mathbf {B} _{r}}$ is the residual flux density, expressed in teslas (T).
• ${\displaystyle \scriptstyle V}$ is the volume (m3) of the magnet.
• ${\displaystyle \scriptstyle \mu _{0}\;=\;4\pi \cdot 10^{-7}}$ H/m is the permeability of vacuum.[3]
Other Languages
Afrikaans: Magnetisasie
العربية: مغنطة
беларуская: Намагнічанасць
български: Намагнитване
Ελληνικά: Μαγνήτιση
español: Magnetización
فارسی: مغناطش
français: Aimantation
한국어: 자기화
हिन्दी: चुम्बकन
hrvatski: Magnetizacija
Bahasa Indonesia: Magnetisasi
עברית: מגנוט
македонски: Магнетизација
मराठी: चुंबकन
Nederlands: Magnetisatie

norsk nynorsk: Magnetisering
polski: Magnetyzacja
svenska: Magnetisering
Türkçe: Mıknatıslanma
Tiếng Việt: Từ hóa