Magnetic energy and electric energy are related by Maxwell's equations. The potential energy of a magnet of magnetic moment, m, in a magnetic field, B, is defined as the mechanical work of magnetic force (actually of magnetic torque) on re-alignment of the vector of the Magnetic dipole moment, and is equal:
while the energy stored in an inductor (of inductance, L) when current, I, is passing via it is
This second expression forms the basis for superconducting magnetic energy storage.
Energy is also stored in a magnetic field. The energy per unit volume in a region of space of permeability, μ, containing magnetic field, B, is:
More generally, if we assume that the medium is paramagnetic or diamagnetic so that a linear constitutive equation exists that relates B and H, then it can be shown that the magnetic field stores an energy of
where the integral is evaluated over the whole region where the magnetic field exists.