Electromagnetic Fields and Waves

# 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:

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

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:

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

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

$\mathbit{B}={\mu }_{0}\mathbit{J}$

For uniform and isotropic fields, magnetising is the following:

$\mathbit{J}=\frac{\chi {B}_{0}}{{\mu }_{0}}$

Where  is a magnetic susceptibility coefficient. Thus,

$\mathbit{B}\mathbf{=}{\mathbit{B}}_{\mathbf{0}}\mathbf{+}{\mathbit{B}}^{\mathbf{‘}}\mathbf{=}{\mathbit{B}}_{\mathbf{0}}\mathbf{+}{\mathbit{\mu }}_{\mathbf{0}}{\mathbit{B}}_{\mathbf{0}}=\left(1+{\mu }_{0}\right){\mathbit{B}}_{\mathbf{0}}\mathbf{=}\mathbit{\mu }{\mathbit{B}}_{\mathbf{0}}$

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.

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