Path Integral Approach to Faraday's Law of Induction

Sami Mohammad Al-Jaber

An-Najah National University.

DOI: 10.4236/jemaa.2011.36030                

Abstract

We derive a general form of the induced electromotive force due to a time-varying magnetic field. It is shown that the integral form of Faraday's law of induction is more conveniently written in the covering space. Thus the differential form is shown to relate the induced electric field in the n^th winding number to the (n+1)^th time-derivative of the magnetic field.

Keywords

Faraday's Law of Induction, Electromotive Force

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	D. Halliday, R. Resnick and K. S. Krane, “Physics,” 5th edition, wiley, New York, 2002.
[2]	R. A. Serway and J. W. Jewett, “Physics for Scientists and Engineers,” Brooks Cole, Belmont, 2009.
[3]	D. C. Giancoli, “Physics for Scientists and Engineers with Modern Physics,” 4th edition, Prentice-Hall, New York, 2008.
[4]	D. J. Griffiths, “Introduction to Electrodynamics,” Prentice-Hall, New York, 1999.
[5]	R. P. Feynman, “Space-time Approach to Non-Relativistic Quantum Mechanics,” Reviews of Modern Physics, Vol. 20, 1948, PP. 367-387. doi:10.1103/RevModPhys.20.367
[6]	C. C. Gerry and V. A. Singh, “Feynman Path Integral Approach to the Aharonov-Bohm Effect,” Physical, Review D, Vol. 20, 1979, PP. 2550-2554. doi:10.1103/PhysRevD.20.2550
[7]	B. Balaji, “Universal Nonlinear Filtering Using Feynma Path Integrals: The Continuous Model With Aditive Noise,” PMC Physics A, Vol. 3, 2009.
[8]	D. Li and A. G. Voth, “Feynman Path Integral Approach For Studying Intermolecular Effects In Proton-Transfer Reactions,” Journal of Physics and Chemestry, Vol. 95, 1999, PP. 10425- 10431.
[9]	S. L. Mielke and D. G. Truhlar, “Improved Methods for Feynman Path Integra Calculations of Vibrational- Rotational Free Energies and Applications to Isotropic Fractionation of Hydrated Chloride Ions,” Journal of Physics and Chemestry, Vol. 113, 2009, PP. 4817-4827.
[10]	P. Storey and C. C. Tannoudji, “The Feynman Path Itegral Approach to Atomic Interferometry,” Journal of Physics, Vol. 4, 1994, PP. 1999-2027. doi:10.1051/jp2:1994103
[11]	L. S. Schulman, “Techniques and Applications of Path Integration,” Wiley, New York, 1981.
[12]	S. M. AL-Jaber and W. C. Henneberger, “The Restricted Rotor: The Effect of Topology on Quantum Mechanics,” Journal of Physics A: Mathematical and General, Vol. 23, 1990, P. 2939. doi:10.1088/0305-4470/23/13/030
[13]	P. Girard and R. Mackenzie, “Altered States: Two Anyons via Path Integrals for Multiply Connected Spaces,” Physics Letters A, Vol. 207, 1995, PP. 17-22.
[14]	D. K. Biss, “A Generalized Approach to the Fundamental Group,” The American Mathematical Monthly, Vol. 107, 2000, PP. 711-720.