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A particle of mass m in a circular orbit of radius r
has an angular momentum 
,
where 
(in the nonrelativistic limit)
is the particle's momentum. Although 
and 
are constantly changing direction, 
is a constant
in the absence of any torques on the system.
If the particle happens to carry an electric charge
as well as a mass (the case shown being an electron
with mass 
and charge -e) then the circulation of that
charge constitutes a current loop which in turn
generates a magnetic moment 
which is
inextricably ``locked'' to the angular momentum:
,
where 
=
J/T
is the Bohr magneton for the case of the electron orbit.
Because the potential energy of a magnetic dipole moment
in a uniform magnetic field 
is given by 
,
the orientation of the orbit in a magnetic field
determines the contribution of its magnetic interaction
to the total energy of the state:
.
This contribution
is much smaller than the difference between ``shells''
with different principle quantum numbers n,
and so it is called `` fine structure''
in atomic spectroscopy.