Exact fields of electrostatic and magnetostatic multipoles

Revista Mexicana de Fisica

Volumn 44, Issue 1, 1998, Pages 24-35

  Kielanowski, Piotr ^a   Loewe, Mark ^b,c  

^a DEPARTAMENTO DE FÍSICA   (Mexico)

^b TEXAS STATE UNIVERSITY   (United States)

^c The University of Texas at Austin   (United States)

Author keywords

Electrostatic field; Magnetostatic field; Multipole expansion; Spherical tensors

Indexed keywords

EID: 0032361418     PISSN: 0035001X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. J.D. Jackson, Classical Electrodynamics, Second edition (Wiley, New York, 1975).
2. J.L. Synge and A. Schild, Tensor Calculus, (University of Toronto Press, Toronto, 1949); D.M. Brink and G.R. Satchler, Angular momentum, (Oxford University Press, London 1962); A.R. Edmonds, Angular momentum in quantum mechanics, Second edition, (Princeton University Press, Princeton, New Jersey, 1960); M.E. Rose, Elementary theory of angular momentum, (Wiley, New York, 1957).
3. J.L. Synge and A. Schild, Tensor Calculus, (University of Toronto Press, Toronto, 1949); D.M. Brink and G.R. Satchler, Angular momentum, (Oxford University Press, London 1962); A.R. Edmonds, Angular momentum in quantum mechanics, Second edition, (Princeton University Press, Princeton, New Jersey, 1960); M.E. Rose, Elementary theory of angular momentum, (Wiley, New York, 1957).
4. J.L. Synge and A. Schild, Tensor Calculus, (University of Toronto Press, Toronto, 1949); D.M. Brink and G.R. Satchler, Angular momentum, (Oxford University Press, London 1962); A.R. Edmonds, Angular momentum in quantum mechanics, Second edition, (Princeton University Press, Princeton, New Jersey, 1960); M.E. Rose, Elementary theory of angular momentum, (Wiley, New York, 1957).
5. J.L. Synge and A. Schild, Tensor Calculus, (University of Toronto Press, Toronto, 1949); D.M. Brink and G.R. Satchler, Angular momentum, (Oxford University Press, London 1962); A.R. Edmonds, Angular momentum in quantum mechanics, Second edition, (Princeton University Press, Princeton, New Jersey, 1960); M.E. Rose, Elementary theory of angular momentum, (Wiley, New York, 1957).
6. G. Ya Lyubarskii, The Application of Group Theory in Physics, (Pergamon Press, Oxford 1960), p. 217.
7. E. Ley-Koo and A. Góngora-T, Rev. Mex. Fís. 34 (1988) 645.
8. Victor Namias, Am J. Phys. 47 (1979) 803.
9. This fact also follows from gauge invariance; see the appendix.
10. Stanley Fenster, Am. J. Phys. 43 (1973) 683.
11. Although the symmetry arguments are more general, this expression may also te obtained by direct integration: (formula presented) where the second equality relies on a trigonometric identity, the third equality relies on the fact that a phase shift has no effect when a periodic function is integrated over one full period, and the fifth equality relies on the fact that only the k = n/2 term in the sum contributes.
12. J.B. Bronzan, Am. J. Phys. 39 (1971) 1357; J.B. Bronzan, in Electromagnetism: paths to research, edited by Doris Teplitz, (Plenum Press, New York, 1982), p. 171; C. G. Gray, Am. J. Phys. 46 (1978) 582; C. G. Gray, Am. J. Phys. 47 (1979) 457; Am. J. Phys. 47 (1979) 1011; A. Castellanos, M. Panizo, and J. Rivas, Am. J. Phys. 46 (1978) 1116; Carl A. Kocher, Am. J. Phys. 46 (1978) 578.
13. J.B. Bronzan, Am. J. Phys. 39 (1971) 1357; J.B. Bronzan, in Electromagnetism: paths to research, edited by Doris Teplitz, (Plenum Press, New York, 1982), p. 171; C. G. Gray, Am. J. Phys. 46 (1978) 582; C. G. Gray, Am. J. Phys. 47 (1979) 457; Am. J. Phys. 47 (1979) 1011; A. Castellanos, M. Panizo, and J. Rivas, Am. J. Phys. 46 (1978) 1116; Carl A. Kocher, Am. J. Phys. 46 (1978) 578.
14. J.B. Bronzan, Am. J. Phys. 39 (1971) 1357; J.B. Bronzan, in Electromagnetism: paths to research, edited by Doris Teplitz, (Plenum Press, New York, 1982), p. 171; C. G. Gray, Am. J. Phys. 46 (1978) 582; C. G. Gray, Am. J. Phys. 47 (1979) 457; Am. J. Phys. 47 (1979) 1011; A. Castellanos, M. Panizo, and J. Rivas, Am. J. Phys. 46 (1978) 1116; Carl A. Kocher, Am. J. Phys. 46 (1978) 578.
15. J.B. Bronzan, Am. J. Phys. 39 (1971) 1357; J.B. Bronzan, in Electromagnetism: paths to research, edited by Doris Teplitz, (Plenum Press, New York, 1982), p. 171; C. G. Gray, Am. J. Phys. 46 (1978) 582; C. G. Gray, Am. J. Phys. 47 (1979) 457; Am. J. Phys. 47 (1979) 1011; A. Castellanos, M. Panizo, and J. Rivas, Am. J. Phys. 46 (1978) 1116; Carl A. Kocher, Am. J. Phys. 46 (1978) 578.
16. J.B. Bronzan, Am. J. Phys. 39 (1971) 1357; J.B. Bronzan, in Electromagnetism: paths to research, edited by Doris Teplitz, (Plenum Press, New York, 1982), p. 171; C. G. Gray, Am. J. Phys. 46 (1978) 582; C. G. Gray, Am. J. Phys. 47 (1979) 457; Am. J. Phys. 47 (1979) 1011; A. Castellanos, M. Panizo, and J. Rivas, Am. J. Phys. 46 (1978) 1116; Carl A. Kocher, Am. J. Phys. 46 (1978) 578.
17. J.B. Bronzan, Am. J. Phys. 39 (1971) 1357; J.B. Bronzan, in Electromagnetism: paths to research, edited by Doris Teplitz, (Plenum Press, New York, 1982), p. 171; C. G. Gray, Am. J. Phys. 46 (1978) 582; C. G. Gray, Am. J. Phys. 47 (1979) 457; Am. J. Phys. 47 (1979) 1011; A. Castellanos, M. Panizo, and J. Rivas, Am. J. Phys. 46 (1978) 1116; Carl A. Kocher, Am. J. Phys. 46 (1978) 578.
18. J.B. Bronzan, Am. J. Phys. 39 (1971) 1357; J.B. Bronzan, in Electromagnetism: paths to research, edited by Doris Teplitz, (Plenum Press, New York, 1982), p. 171; C. G. Gray, Am. J. Phys. 46 (1978) 582; C. G. Gray, Am. J. Phys. 47 (1979) 457; Am. J. Phys. 47 (1979) 1011; A. Castellanos, M. Panizo, and J. Rivas, Am. J. Phys. 46 (1978) 1116; Carl A. Kocher, Am. J. Phys. 46 (1978) 578.