# Magnetic energy

Magnetic energy and electrostatic potential energy are related by Maxwell's equations. The potential energy of a magnet of magnetic moment $\mathbf$ in a magnetic field $\mathbf$ 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:

$E_{\rm }=-\mathbf \cdot \mathbf$ while the energy stored in an inductor (of inductance $L$ ) when a current $I$ flows through it is given by:

$E_{\rm }={\frac }LI^$ .

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 $\mu _$ containing magnetic field $\mathbf$ is:

$u={\frac }{\frac }{\mu _}}$ More generally, if we assume that the medium is paramagnetic or diamagnetic so that a linear constitutive equation exists that relates $\mathbf$ and $\mathbf$ , then it can be shown that the magnetic field stores an energy of

$E={\frac }\int \mathbf \cdot \mathbf \ \mathrm V$ where the integral is evaluated over the entire region where the magnetic field exists.