## Magnetization

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**Magnetization** is a vector physical quantity that characterizes the magnetic state of a macroscopic physical body. Usually designated *M.* Defined as the magnetic moment per unit volume of a substance:

M = pm V {\displaystyle \mathbf {M} ={\frac {\mathbf {p_{m}} }{V}}}

Here, **M** is the magnetization vector; **pm {\displaystyle p_{m}}** is the magnetic moment vector; V is volume.

In the general case (the case of a non-uniform, for one reason or another, medium) magnetization is expressed as

M = dpmd V {\displaystyle \mathbf {M} ={\frac {d\mathbf {p_{m}} }{dV}}}

and is a function of coordinates. Where dpm {\displaystyle dp_{m}} is the total magnetic moment of molecules in the volume **dV.**

The relationship between **M** and magnetic field strength **H** in diamagnetic and paramagnetic materials is usually linear (at least when the magnetizing field is not too large):

M = χ m H {\displaystyle \mathbf {M} =\chi _{m}\mathbf {H} } ,

where *χ* m is called magnetic susceptibility. In ferromagnetic materials there is no unambiguous relationship between **M** and **H** due to magnetic hysteresis, and the magnetic susceptibility tensor is used to describe the dependence.

Magnetic induction is defined through magnetization as:

B = μ 0 ( H + M ) {\displaystyle \mathbf {B} =\mu _{0}\mathbf {(H+M)} } (SI system) B = ( H + 4 π M ) {\ displaystyle \mathbf {B} =(\mathbf {H} +4\pi \mathbf {M} )} (in the GHS system)

### See also[ | ]

- Residual magnetization

### Literature[ | ]

- Magnetization // Great Soviet Encyclopedia: [in 30 volumes] / ch. ed. A. M. Prokhorov. — 3rd ed. - M.: Soviet Encyclopedia, 1969-1978.
*Vonsovsky S.V.*Magnetism, M., 1971*Kirensky L.V.*Magnetism, 3rd ed., M., 1967.*Savelyev I.V.*Electricity and magnetism, 2001.

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