The magnetic field of current-carrying polygons: An application of vector field rotations

American Journal of Physics

Volumn 68, Issue 5, 2000, Pages 469-474

  Grivich, Matthew I ^a   Jackson, David P ^a  

^a SANTA CLARA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034418345     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.19461     Document Type: Article

References (13)

1. Paul A. Tipler, Physics for Scientists and Engineers (Worth, New York, 1991), pp. 815-825.
2. David J. Griffiths, Introduction to Electrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1981), pp. 184-189.
3. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975), pp. 177-180.
4. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, Elmsford, 1984). p. 112.
5. We were not able to find any texts that discussed vector field rotations. We thank one of the referees for supplying us with Refs. 9 and 10.
6. George Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, San Diego, 1985) p. 264.
7. One of the main difficulties when working with coordinate rotations is to assume that the value of the function ψ(x) moves from x to Rx under the rotation. When viewed in the unprimed coordinate system, ψ(x) is actually replaced by ψ(Rx), which means that the value ψ(Rx) has moved from Rx to x.
8. George Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, San Diego, 1985), p. 201.
9. S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Row, Peterson, Evanston, 1961), p. 31.
10. J. M. Blatt and V. F. Weiskopf, Theoretical Nuclear Physics (Wiley, New York, 1952), p. 796.
11. We have made the variable substitutions x' = x/R, y' = y/R, z' = zlR and then dropped the primes.
12. z plots. The difference is less than 1% and was chosen to make the local maxima visible.
13. David J. Griffiths, Introduction to Electrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1981), pp. 212-213.