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Magnetic energy and electrostatic potential energy are related by Maxwell's equations. The potential energy of a magnet or magnetic moment m {\displaystyle \mathbf {m} } in a magnetic field B {\displaystyle \mathbf {B} } is defined as the mechanical work of the magnetic force on the re-alignment of the vector of the magnetic dipole moment and is equal to:
Energy is also stored in a magnetic field. The energy per unit volume in a region of space of permeability μ 0 {\displaystyle \mu _{0}} containing magnetic field B {\displaystyle \mathbf {B} } is:
More generally, if we assume that the medium is paramagnetic or diamagnetic so that a linear constitutive equation exists that relates B {\displaystyle \mathbf {B} } and H {\displaystyle \mathbf {H} } , then it can be shown that the magnetic field stores an energy of
For a magnetostatic system of currents in free space, the stored energy can be found by imagining the process of linearly turning on the currents and their generated magnetic field, arriving at a total energy of: