Formula: Magnetic Flux density (B-field) and H-field
$$\class{violet}{B} ~=~ \mu_0 \, \mu_{\text r} \, \class{violet}{H}$$
$$\class{violet}{B} ~=~ \mu_0 \, \mu_{\text r} \, \class{violet}{H}$$
$$\class{violet}{H} ~=~ \frac{ \class{violet}{B} }{\mu_0 \, \mu_{\text r}}$$
$$\mu_{\text r} ~=~ \frac{ \class{violet}{B} }{\mu_0 \, \class{violet}{H}}$$
$$\mu_0 ~=~ \frac{ \class{violet}{B} }{\mu_{\text r} \, \class{violet}{H}}$$
Magnetic flux density (B-field)
$$ \class{violet}{B} $$ Unit $$ \mathrm{T} = \frac{\mathrm{kg}}{\mathrm{A} \, \mathrm{s}^2} $$
Magnetic flux density (short: magnetic field) describes the amount of the magnetic flux that penetrates an area.
Magnetic field (H-field)
$$ \class{violet}{H} $$ Unit $$ \frac{ \mathrm A }{ \mathrm m } $$
The H-field describes the strength of the magnetic field.
Note: The formula is only valid if \(\class{violet}{B}\) and \(H\) are parallel to each other!
Relative permeability
$$ \mu_{\text r} $$ Unit $$ - $$
The relative permeability takes into account the medium (e.g. water, iron) in which the magnetic flux density is to be calculated.
This formula assumes that the medium is linear, homogeneous, isotropic and time-invariant.
Vacuum permeability
$$ \mu_0 $$ Unit $$ \frac{\mathrm{Vs}}{\mathrm{Am}} = \frac{ \mathrm{kg} \, \mathrm{m} }{ \mathrm{A}^2 \, \mathrm{s}^2 } $$The vacuum permeability is a physical constant and has the following experimentally determined value:
$$ \mu_0 ~=~ 1.256 \, 637 \, 062 \, 12 ~\cdot~ 10^{-6} \, \frac{\mathrm{Vs}}{\mathrm{Am}} $$