is defined as the mechanical work of the magnetic force on the re-alignment of the vector of the magnetic dipole moment and is equal to:
The mechanical work takes the form of a torque
which will act to "realign" the magnetic dipole with the magnetic field.
[1] In an electronic circuit the energy stored in an inductor (of inductance
This expression forms the basis for superconducting magnetic energy storage.
It can be derived from a time average of the product of current and voltage across an inductor.
Energy is also stored in a magnetic field itself.
The energy per unit volume
in a region of free space with vacuum permeability
More generally, if we assume that the medium is paramagnetic or diamagnetic so that a linear constitutive equation exists that relates
is the magnetic permeability of the material), then it can be shown that the magnetic field stores an energy of
where the integral is evaluated over the entire region where the magnetic field exists.
[2] 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:[2]
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.
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