Magnetic energy

Magnetic energy and electrostatic potential energy are related by Maxwell's equations. The potential energy of a magnet or 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:
$E_\text = -\mathbf \cdot \mathbf$
while the energy stored in an inductor (of inductance $L$) when a current $I$ flows through it is given by:
$E_\text = \frac LI^2.$
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 $\mu _0$ containing magnetic field $\mathbf$ is:
$u = \frac \frac$

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
$E = \frac \int \mathbf \cdot \mathbf \, \mathrmV$
where 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:
$E = \frac \int \mathbf \cdot \mathbf\, \mathrmV$
where $\mathbf$ is the current density field and $\mathbf$ is the magnetic vector potential. This is analogous to the electrostatic energy expression $\frac\int \rho \phi \, \mathrmV$; 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.

Forms of energy
Magnetism

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