Formula Magnetic Energy Stored in B-Field Magnetic energy Magnetic field Volume Vacuum permeability
$$W_{\text m} ~=~ \frac{1}{2\, \mu_0} \, V \, \class{violet}{B}^2$$ $$W_{\text m} ~=~ \frac{1}{2\, \mu_0} \, V \, \class{violet}{B}^2$$ $$\class{violet}{B} ~=~ \frac{ 2 \, \mu_0 \, W_{\text m}}{ V }$$ $$V ~=~ \frac{ 2 \, \mu_0 \, W_{\text m}}{ \class{violet}{B} }$$
Magnetic energy
$$ W_{\text m} $$ Unit $$ \mathrm{J} $$ Magnetic energy contained in a region of space where a B-field is present.
Magnetic field
$$ \class{violet}{B} $$ Unit $$ \mathrm{T} = \frac{\mathrm{kg}}{\mathrm{A} \, \mathrm{s}^2} $$ Magnetic field in a certain region of space in which magnetic energy is stored.
Volume
$$ V $$ Unit $$ \mathrm{m}^3 $$ Volume of a considered region of space for which the magnetic energy is to be calculated.
Vacuum permeability
$$ \mu_0 $$ Unit $$ \frac{\mathrm{Vs}}{\mathrm{Am}} = \frac{ \mathrm{kg} \, \mathrm{m} }{ \mathrm{A}^2 \, \mathrm{s}^2 } $$ Magnetic field constant is a physical constant and occurs whenever magnetic fields are involved. It has the value \( \mu_0 = 4\pi \cdot 10^{-7} \, \frac{ \mathrm{N} }{ \mathrm{A}^2 } \).