Orbital Angular Momentum

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.

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• Magnetic Interactions