Electrically induced magnetic fields; A consistent approach

American Journal of Physics

Volumn 71, Issue 9, 2003, Pages 925-929

  Batell, Brian ^a   Ferstl, Andrew ^a  

^a WINONA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042762222     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1586260     Document Type: Article

References (17)

1. See R. A. Serway and R. J. Biechner, Physics for Scientists and Engineers, 5th ed. (Harcourt College Publishers, Orlando, FL, 2000), pp. 993-994 as an example of how many introductory texts perform this calculation.
2. See D. J. Griffiths, Introduction to Electrodynamics, 3rd ed. (Prentice Hall, Upper Saddle River, NJ, 1999), p. 308. Griffiths explains the quasistatic approximation. Also see R. L. Reese, University Physics (Brooks/Cole Publishing Co., Pacific Grove, CA, 2000), pp. 895-952 for a consistent approach; Reese introduces Faraday's law concurrently with Maxwell's equations and electromagnetic radiation. Also see R. Wolfson and J. M. Pasachoff, Physics, 2nd ed. (Harper Collins College Publishers, New York, 1995), p. 799 for an acknowledgement of the approximation.
3. See D. J. Griffiths, Introduction to Electrodynamics, 3rd ed. (Prentice Hall, Upper Saddle River, NJ, 1999), p. 308. Griffiths explains the quasistatic approximation. Also see R. L. Reese, University Physics (Brooks/Cole Publishing Co., Pacific Grove, CA, 2000), pp. 895-952 for a consistent approach; Reese introduces Faraday's law concurrently with Maxwell's equations and electromagnetic radiation. Also see R. Wolfson and J. M. Pasachoff, Physics, 2nd ed. (Harper Collins College Publishers, New York, 1995), p. 799 for an acknowledgement of the approximation.
4. See D. J. Griffiths, Introduction to Electrodynamics, 3rd ed. (Prentice Hall, Upper Saddle River, NJ, 1999), p. 308. Griffiths explains the quasistatic approximation. Also see R. L. Reese, University Physics (Brooks/Cole Publishing Co., Pacific Grove, CA, 2000), pp. 895-952 for a consistent approach; Reese introduces Faraday's law concurrently with Maxwell's equations and electromagnetic radiation. Also see R. Wolfson and J. M. Pasachoff, Physics, 2nd ed. (Harper Collins College Publishers, New York, 1995), p. 799 for an acknowledgement of the approximation.
5. See Ref. 1, pp. 979-1013. The fact that changing electric fields induce magnetic fields is only briefly mentioned on pp. 1000; the approximation is not recognized anywhere else in the chapter. Also see P. A. Tipler, Physics, 4th ed. (W. H. Freeman and Co., New York, 1999), pp. 927-958; V. D. Barger and M. G. Olsson, Classical Electricity and Magnetism (Allyn and Bacon, Inc., Newton, MA, 1987), pp. 240-280. The approximation is not mentioned in either book in the chapter covering Faraday's law.
6. See Ref. 1, pp. 979-1013. The fact that changing electric fields induce magnetic fields is only briefly mentioned on pp. 1000; the approximation is not recognized anywhere else in the chapter. Also see P. A. Tipler, Physics, 4th ed. (W. H. Freeman and Co., New York, 1999), pp. 927-958; V. D. Barger and M. G. Olsson, Classical Electricity and Magnetism (Allyn and Bacon, Inc., Newton, MA, 1987), pp. 240-280. The approximation is not mentioned in either book in the chapter covering Faraday's law.
7. T. A. Abbott and D. J. Griffiths, "Acceleration without radiation, " Am. J. Phys. 53 (12), 1203-1204 (1985), and C. Thevenet, "Electromagnetic radiation from sinusoidal currents, " Am. J. Phys. 67, 120-124 (1999).
8. T. A. Abbott and D. J. Griffiths, "Acceleration without radiation, " Am. J. Phys. 53 (12), 1203-1204 (1985), and C. Thevenet, "Electromagnetic radiation from sinusoidal currents, " Am. J. Phys. 67, 120-124 (1999).
9. See also integral derivation of differential equations in the Appendix. Introductory texts generally rely on integrals.
10. s + ε, and take the limit as ε→0. Since the electric field is continuous, the last term is zero, and you are left with the boundary condition.
11. 0 where, for our problem, the charge density is 0.
12. Equations (8) and (9) are actually the Green's function for Eq. (7) with an arbitrary source term.
13. I. S. Gradshteyn and I. M. Ryzhik. Table of Integrals, Series, and Products (Academic, Orlando, FL, 1980), p. 967.
14. Reference 8, p. 969.
15. 2; for an infinite solenoid with cylindrical symmetry, the power radiated per unit area should fall off as 1/r.
16. (1) would have been the solution.
17. The calculation of the self-capacitance of a finite solenoid is not the main focus of this paper. The interested reader can see R. G. Medhurst. Resistance and Self-Capacitance of Single-Layer Solenoids, Wireless Engineer, February 1947, pp. 35-43 and March 1947, pp. 80-92.