The angular momentum of a steady, axially symmetric distribution of electromagnetic fields is shown to be expressible as , where is an element of moving charge at position and is the local vector potential. This result, which is valid for relativistic motion, gives an easy way of calculating the angular momentum of symmetric distributions of charges or currents. A consequence of this result is that in the nonrelativistic limit, the magnetic energy of the distribution can be expressed solely in terms of the angular momentum and the angular velocity of the rotating system, , as . This result is applied to three uniform, nonrelativistic, spinning charge distributions: a cylindrical shell, a spherical shell, and a solid sphere.
REFERENCES
1.
R. P.
Feynman
, R. B.
Leighton
, and M.
Sands
, The Feynman Lectures on Physics
(Addison-Wesley
, Menlo Park, CA, 1970
), Vol. II
, Chaps. 26–28.2.
P.
Lorrain
, D. R.
Corson
, and D. R.
Lorrain
, Electromagnetic Fields and Waves
(Freeman
, New York, 1988
), 3rd ed.3.
4.
5.
J. R.
Reitz
, F. J.
Milford
, and R. W.
Christy
, Foundations of Electromagnetic Theory
(Addison-Wesley
, Reading, MA, 1979
), 3rd ed.6.
D. J.
Griffiths
, Introduction to Electrodynamics
(Prentice Hall
, Englewood Cliffs, NJ, 1981
).7.
8.
F. E.
Low
, Classical Field Theory
(Wiley
, New York, 1997
), Sec. 2.6.9.
10.
J. M.
Eisenberg
and W.
Greiner
, Nuclear Theory: Excitation Mechanisms
(North Holland
, Amsterdam, 1988
), 3rd ed., Vol. 2
.11.
J. S.
Marsh
, “Magnetic and electric fields of rotating charge distributions
,” Am. J. Phys.
50
(1
), 51
–53
(1982
).12.
H. P.
Siegel
, “Inadequacy of the gyromagnetic theorem
,” Am. J. Phys.
44
(4
), 344
–347
(1976
).13.
B. R.
Casserberg
, “Electromagnetic momentum introduced simply
,” Am. J. Phys.
50
(5
), 425
–416
(1982
).14.
G. R.
Fowles
, “Momentum conservation and the vector potential of moving charges
,” Am. J. Phys.
48
(9
), 779
–780
(1980
).15.
E.
Corinaldesi
, “Angular momentum of a static electromagnetic field
,” Am. J. Phys.
48
(1
), 83
–84
(1980
).16.
N.
Gauthier
, “A Newton-Faraday approach to electromagnetic energy and angular momentum storage in an electromechanical system
,” Am. J. Phys.
70
(10
), 1034
–1038
(2002
).17.
A. S.
de Castro
, “Electromagnetic angular momentum for a rotating charged shell
,” Am. J. Phys.
59
(2
), 180
–181
(1991
).© 2006 American Association of Physics Teachers.
2006
American Association of Physics Teachers
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