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Solenoidality of a magnetic induction field and conservation of total momentum
Type
Oral presentation
Language
English
Obiettivo Specifico
5.9. Formazione e informazione
Status
Submitted
Conference Name
Issued date
September 26, 2011
Conference Location
L’Aquila, Italia.
Abstract
The present comunication discusses the physical aspects of a system of non-relativistic massive charge particles moving within an electromagnetic field (e.m.), which propagates through the entire space. The role of total momentum conservation on the solenoidality of a magnetic induction field is demonstrated. After a careful review of all the more widely sustained didactic justifications for the solenoidality of magnetic induction, some properties of the Maxwell stress tensor are defined according to Minkowsky. This comunication presents a new framework wherein the necessary condition for the free-divergence of induction derives directly from the total momentum conservation of the system, i.e. particles and field.
References
[1] L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Fourth Revised English Edition, Course of Theoretical Physics, Volume 2 (Butterworth-Heinemann, Oxford, 1975), 402 pp..
[2] L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, Second Edition, Course of Theoretical Physics, Volume 8 (Butterworth-Heinemann, Oxford, 1984), 460 pp. (1984).
[3] D. E. Soper, Classical Field Theory (Dover Publication, New York, 2008), 272 pp..
[4] B. R. Casserberg, “Electromagnetic momentum introduced simply”, Am. J. Phys., 50 (5), 415 (1982).
[5] R. H. Romer, “Electromagnetic field momentum”, Am. J. Phys. 63 (9), 777 (1995).
[6] T. H. Boyer, “Connecting linear momentum and energy for electromagnetic systems”, Am. J. Phys., 74 (8), 742 (2006).
[7] S. Ragusa, “Electromagnetic energy and momentum balance for surface charge distributions”, Am. J. Phys., 58 (4), 364 (1990).
[8] J. M. Aguirregabiria, A. Hernández, and M. Rivas, “On dynamical equations and conservation laws in quasistatic electromagnetic systems”, Am. J. Phys., 58 (7), 635 (1990).
[9] J. Paton, “Field energy and momentum, and motion of a charged particle in a static electromagnetic field”, Eur. J. Phys., 13 (6), 280 (1992).
[10] G. H. Goedecke, “On electromagnetic conservation laws”, Am. J. Phys., 68 (4), 380 (2000).
[11] N. Gauthier, “What happens to energy and momentum when two oppositely-moving wave pulses overlap?”, Am. J. Phys., 71 (8), 787 (2003).
[12] A. L. Kholmetskii, “Apparent paradoxes in classical electrodynamics: the energy–momentum conservation law for a bound electromagnetic field”, Eur. J. Phys., 27 (4), 825 (2006).
[13] G. T. Hooft, “Magnetic monopoles in unified gauge theories”, Nuclear Physics B, 79 (2), 276-284 (1974).
[14] P. B. Price, E. K. Shirk, W. Z. Osborne, L. S. Pinsky, “Evidence for Detection of a Moving Magnetic Monopole”, Phys. Rev. Lett. 35 (8), 487–490 (1975).
[15] P. T. Leung, “Magnetic monopole and Poynting’s theorem”, Eur. J. Phys., 16 (1), 43 (1995).
[16] Jun S. Song, “Theory of Magnetic Monopoles and Electric-Magnetic Duality: A Prelude to S-Duality”, J. Undergrad. Sci. 3, 47-55 (1996).
[17] Z. Fang, N. Nagaosa, K. S. Takahashi, A. Asamitsu, R. Mathieu, T. Ogasawara, H. Yamada, M. Kawasaki, Y. Tokura, K. Terakura, “The Anomalous Hall Effect and Magnetic Monopoles in Momentum-Space”, Science, 302 (5642), 92-95 (2003).
[18] J. D. Jackson, Classical Electrodynamics, Third Edition (John Wiley&Son, New York, 1998), 832 pp..
[19] H. Minkowski, Nachr. Ges. Wiss. Gottingen, 53 (1908); ibid., Math. Ann., 68, 472 (1910).
[20] M. Abraham, Rend. Circ. Matem. Palermo, 28, 1 (1909); ibid. 30, 5 (1910).
[21] A. Einstein, and J. Laub, “Über die im elektromagnetischen Felde auf ruhende Körper ausgeübten ponderomotorischen Kräfte”, Ann. Phys. (Leipzig) 331 (8), 541–550 (1908).
[22] P. Penfield Jr., and H. A. Haus, Electrodynamics of Moving Media, Research Monograph No. 40 (MIT Press, Cambridge, Massachusetts, 1967); ibid., Special Technical Report No. 14, Research Laboratory of Electronics, Massachusetts Institute of Technology (1967).
[23] J. P., Gordon, “Radiation Forces and Momenta in Dielectric Media”, Phys. Rev. A, 8 (1), 14-21 (1973).
[24] R. Peierls, “The Momentum of Light in a Refracting Medium”, in Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 347 (1651), 475-491 (1976).
[25] D. F. Nelson, “Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy”, Phys. Rev. A, 44 (6), 3985-3966 (1991).
[26] R. Loudon, L. Allen, and D. F. Nelson, “Propagation of electromagnetic energy and momentum through an absorbing dielectric”, Phys. Rev. E, 55 (1), 1071-1085 (1997).
[27] Y. N. Obukhov, and F. W. Hehl, “Electromagnetic energy–momentum and forces in matter”, Phys. Lett. A, 311 (4-5), 277–284 (2003).
[28] M. Mansuripur, “Radiation pressure and the linear momentum of the electromagnetic field”, Opt. Express, 12 (22), 5375-5401 (2004).
[29] M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Centini, C. Sibilia, and J. W. Haus, “Radiation pressure of light pulses and conservation of linear momentum in dispersive media”, Phys. Rev. E, 73 (5), 056604 [12 pp.] (2006).
[30] S. M. Barnett, “Resolution of the Abraham–Minkowski Dilemma”, Phys. Rev. Lett. 104 (7), 070401 [4 pp.] (2010).
[31] J. L. Jiménez, I. Campos, and M. A. López-Marino, “A new perspective of the Abraham-Minkowski controversy”, Eur. Phys. J. Plus 126 (5), 50 [11 pp.] (2011).
[32] R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Constraining Validity of the Minkowski Energy–Momentum Tensor”, Phys. Rev. A 79 (2), 023813 [7 pp.] (2009).
[33] L. Dallen, and D. E. Neuenschwander, “Noether’s theorem in a rotating reference frame”, Am. J. Phys. 79 (3), 326 (2011).
[34] A. Avvantaggiati, Istituzioni di Matematica (Casa Editrice Ambrosiana CEA, Exclusive distributor Zanichelli, Roma, 1991), XIV 798 pp..
[35] C. Mencuccini, V. Silvestrini, Fisica II, Elettromagnetismo – Ottica, Corso di fisica per le facoltà scientifiche corredato di esempi ed esercizi, New expanded edition (Liguori Editore, Roma, 1999), 836 pp..
[36] S. Bobbio, E. Gatti, Elettromagnetismo Ottica – Programma di Matematica, Fisica, Elettronica (Bollati Boringhieri Editore, Torino, 1991), 827 pp..
[37] L. Page, and N. I. Adams Jr., “Action and Reaction between Moving Charges”, Am. J. Phys. 13, 141 (1945),
[38] R. Schlegel, “Radiation Pressure on a Rapidly Moving Surface”, Am. J. Phys. 28 (8) 687 (1960).
[39] T. H. Boyer, “Energy and Momentum in Electromagnetic Field for Charged Particles Moving with Constant Velocities”, Am. J. Phys., 39 (3) 257 (1971);
[40] F. Herrmann, and G. B. Schmid, “Momentum flow in the electromagnetic field”, Am. J. Phys., 53 (5), 415 (1985).
[41] G. Gerosa, P. Lampariello, Lezioni di Campi Elettromagnetici (Edizioni Ingegneria 2000, Roma, 1995), 489 pp..
[2] L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, Second Edition, Course of Theoretical Physics, Volume 8 (Butterworth-Heinemann, Oxford, 1984), 460 pp. (1984).
[3] D. E. Soper, Classical Field Theory (Dover Publication, New York, 2008), 272 pp..
[4] B. R. Casserberg, “Electromagnetic momentum introduced simply”, Am. J. Phys., 50 (5), 415 (1982).
[5] R. H. Romer, “Electromagnetic field momentum”, Am. J. Phys. 63 (9), 777 (1995).
[6] T. H. Boyer, “Connecting linear momentum and energy for electromagnetic systems”, Am. J. Phys., 74 (8), 742 (2006).
[7] S. Ragusa, “Electromagnetic energy and momentum balance for surface charge distributions”, Am. J. Phys., 58 (4), 364 (1990).
[8] J. M. Aguirregabiria, A. Hernández, and M. Rivas, “On dynamical equations and conservation laws in quasistatic electromagnetic systems”, Am. J. Phys., 58 (7), 635 (1990).
[9] J. Paton, “Field energy and momentum, and motion of a charged particle in a static electromagnetic field”, Eur. J. Phys., 13 (6), 280 (1992).
[10] G. H. Goedecke, “On electromagnetic conservation laws”, Am. J. Phys., 68 (4), 380 (2000).
[11] N. Gauthier, “What happens to energy and momentum when two oppositely-moving wave pulses overlap?”, Am. J. Phys., 71 (8), 787 (2003).
[12] A. L. Kholmetskii, “Apparent paradoxes in classical electrodynamics: the energy–momentum conservation law for a bound electromagnetic field”, Eur. J. Phys., 27 (4), 825 (2006).
[13] G. T. Hooft, “Magnetic monopoles in unified gauge theories”, Nuclear Physics B, 79 (2), 276-284 (1974).
[14] P. B. Price, E. K. Shirk, W. Z. Osborne, L. S. Pinsky, “Evidence for Detection of a Moving Magnetic Monopole”, Phys. Rev. Lett. 35 (8), 487–490 (1975).
[15] P. T. Leung, “Magnetic monopole and Poynting’s theorem”, Eur. J. Phys., 16 (1), 43 (1995).
[16] Jun S. Song, “Theory of Magnetic Monopoles and Electric-Magnetic Duality: A Prelude to S-Duality”, J. Undergrad. Sci. 3, 47-55 (1996).
[17] Z. Fang, N. Nagaosa, K. S. Takahashi, A. Asamitsu, R. Mathieu, T. Ogasawara, H. Yamada, M. Kawasaki, Y. Tokura, K. Terakura, “The Anomalous Hall Effect and Magnetic Monopoles in Momentum-Space”, Science, 302 (5642), 92-95 (2003).
[18] J. D. Jackson, Classical Electrodynamics, Third Edition (John Wiley&Son, New York, 1998), 832 pp..
[19] H. Minkowski, Nachr. Ges. Wiss. Gottingen, 53 (1908); ibid., Math. Ann., 68, 472 (1910).
[20] M. Abraham, Rend. Circ. Matem. Palermo, 28, 1 (1909); ibid. 30, 5 (1910).
[21] A. Einstein, and J. Laub, “Über die im elektromagnetischen Felde auf ruhende Körper ausgeübten ponderomotorischen Kräfte”, Ann. Phys. (Leipzig) 331 (8), 541–550 (1908).
[22] P. Penfield Jr., and H. A. Haus, Electrodynamics of Moving Media, Research Monograph No. 40 (MIT Press, Cambridge, Massachusetts, 1967); ibid., Special Technical Report No. 14, Research Laboratory of Electronics, Massachusetts Institute of Technology (1967).
[23] J. P., Gordon, “Radiation Forces and Momenta in Dielectric Media”, Phys. Rev. A, 8 (1), 14-21 (1973).
[24] R. Peierls, “The Momentum of Light in a Refracting Medium”, in Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 347 (1651), 475-491 (1976).
[25] D. F. Nelson, “Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy”, Phys. Rev. A, 44 (6), 3985-3966 (1991).
[26] R. Loudon, L. Allen, and D. F. Nelson, “Propagation of electromagnetic energy and momentum through an absorbing dielectric”, Phys. Rev. E, 55 (1), 1071-1085 (1997).
[27] Y. N. Obukhov, and F. W. Hehl, “Electromagnetic energy–momentum and forces in matter”, Phys. Lett. A, 311 (4-5), 277–284 (2003).
[28] M. Mansuripur, “Radiation pressure and the linear momentum of the electromagnetic field”, Opt. Express, 12 (22), 5375-5401 (2004).
[29] M. Scalora, G. D’Aguanno, N. Mattiucci, M. J. Bloemer, M. Centini, C. Sibilia, and J. W. Haus, “Radiation pressure of light pulses and conservation of linear momentum in dispersive media”, Phys. Rev. E, 73 (5), 056604 [12 pp.] (2006).
[30] S. M. Barnett, “Resolution of the Abraham–Minkowski Dilemma”, Phys. Rev. Lett. 104 (7), 070401 [4 pp.] (2010).
[31] J. L. Jiménez, I. Campos, and M. A. López-Marino, “A new perspective of the Abraham-Minkowski controversy”, Eur. Phys. J. Plus 126 (5), 50 [11 pp.] (2011).
[32] R. N. C. Pfeifer, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Constraining Validity of the Minkowski Energy–Momentum Tensor”, Phys. Rev. A 79 (2), 023813 [7 pp.] (2009).
[33] L. Dallen, and D. E. Neuenschwander, “Noether’s theorem in a rotating reference frame”, Am. J. Phys. 79 (3), 326 (2011).
[34] A. Avvantaggiati, Istituzioni di Matematica (Casa Editrice Ambrosiana CEA, Exclusive distributor Zanichelli, Roma, 1991), XIV 798 pp..
[35] C. Mencuccini, V. Silvestrini, Fisica II, Elettromagnetismo – Ottica, Corso di fisica per le facoltà scientifiche corredato di esempi ed esercizi, New expanded edition (Liguori Editore, Roma, 1999), 836 pp..
[36] S. Bobbio, E. Gatti, Elettromagnetismo Ottica – Programma di Matematica, Fisica, Elettronica (Bollati Boringhieri Editore, Torino, 1991), 827 pp..
[37] L. Page, and N. I. Adams Jr., “Action and Reaction between Moving Charges”, Am. J. Phys. 13, 141 (1945),
[38] R. Schlegel, “Radiation Pressure on a Rapidly Moving Surface”, Am. J. Phys. 28 (8) 687 (1960).
[39] T. H. Boyer, “Energy and Momentum in Electromagnetic Field for Charged Particles Moving with Constant Velocities”, Am. J. Phys., 39 (3) 257 (1971);
[40] F. Herrmann, and G. B. Schmid, “Momentum flow in the electromagnetic field”, Am. J. Phys., 53 (5), 415 (1985).
[41] G. Gerosa, P. Lampariello, Lezioni di Campi Elettromagnetici (Edizioni Ingegneria 2000, Roma, 1995), 489 pp..
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