Magnetic energy
Introduction '''Magnetic energy''' and electrostatic potential energy are related by Maxwell's equations. The potential energy of a magnet or magnetic moment  in a magnetic field  is defined as the mechanical work of the magnetic force (actually magnetic torque) on the re-alignment of the vector of the magnetic dipole moment and is equal to: while the energy stored in an inductor (of inductance ) when a current  flows through it is given by: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  containing magnetic field  is:More generally, if we assume that the medium is paramagnetic or diamagnetic so that a linear constitutive equation exists that relates  and the magnetization , then it can be shown that the magnetic field stores an energy ofwhere the integral is evaluated over the entire region where the magnetic field exists.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:where  is the current density field and  is the magnetic vector potential. This is analogous to the electrostatic energy expression ; note that neither of these static expressions apply in the case of time-varying charge or current distributions.
References
External links *  Magnetic Energy, Richard Fitzpatrick Professor of Physics The University of Texas at Austin.