# Magnetic energy

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:

${\displaystyle E_{\rm {p,m}}=-\mathbf {m} \cdot \mathbf {B} }$

while the energy stored in an inductor (of inductance, L) when current, I, is passing via it is

${\displaystyle E_{\rm {p,m}}={1 \over 2}LI^{2}}$.

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:

${\displaystyle u={1 \over 2}{B^{2} \over \mu }}$

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

${\displaystyle E={1 \over 2}\int \mathbf {H} \cdot \mathbf {B} \ dV}$

where the integral is evaluated over the whole region where the magnetic field exists.[1]

## References

1. ^ Jackson, John David (1998). Classical Electrodynamics (3rd ed.). New York: Wiley. p. 213. ISBN 0-471-30932-X.