Matter magnetisation

Let’s consider the solenoid that creates a magnetic field when DC current goes through the coil. The field in the solenoid is uniform, and it is proportional to the current through the coil:

$B_0={\mu }_{0}nI.$

If there is any substance in the solenoid, its magnetic field will change:

$\mathit{B}\mathbf{=}{\mathit{B}}_{\mathbf{0}}\mathbf{+}{\mathit{B}}^{\mathbf{‘}}\mathbf{.}$

As soon as this field is characterised by a bigger intensity close to the nucleus, we have to use the average distributed magnetic field for calculations. To describe the magnetic field correctly, which is created by the micro-currents in the fragment of substance, we must consider the magnetising vector of substance:

$\mathit{J}=\frac{{\sum }_i{p}_{m}i}{∆V}$

The magnetising vector is a local characteristic, and can vary in different points of substance. This characteristic helps to determine the magnetic field:

$\mathit{B}={\mu }_0\mathit{J}$

For uniform and isotropic fields, magnetising is the following:

$\mathit{J}=\frac{\chi B_0}{{\mu }_0}$

Where  is a magnetic susceptibility coefficient. Thus,

$\mathit{B}\mathbf{=}{\mathit{B}}_{\mathbf{0}}\mathbf{+}{\mathit{B}}^{\mathbf{‘}}\mathbf{=}{\mathit{B}}_{\mathbf{0}}\mathbf{+}{\mathit{\mu }}_{\mathbf{0}}{\mathit{B}}_{\mathbf{0}}=(1+{\mu }_0){\mathit{B}}_{\mathbf{0}}\mathbf{=}\mathit{\mu }{\mathit{B}}_{\mathbf{0}}$

The parameter  shows how the magnetic field in the substance differs from magnetic fields in a vacuum –

$\mu =\frac{B}{B_0}$

is a magnetic permittivity.

Magnetic types