Methods for calculating the magnetic field of rotating charge distribution with spherical symmetry
DOI:
https://doi.org/10.26577/RCPh-2019-i3-10Keywords:
NNLOT, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan, magnetic field, Maxwell equations, Laplace equation, Marsh’s methodAbstract
The paper considers the methods for finding the magnetic field of a rotating and uniformly charged sphere. Special attention is drawn to the relatively new so-called March method, which can be used for a wide class of problems. This method makes it easy to find solutions for problems with complex conditions. Here the method is applied for a simple spherically symmetric case, the solutions of which are known. All calculations are shown in detail, with a full analysis of analytical calculations. A comparison is made with the known methods for finding the magnetic field for rotating charged spheres. It is shown how using the Marsh method one can construct force lines of the magnetic field in “Wolfram Mathematica” package. The work pursues pedagogical goals and is dedicated to students, undergraduates, Ph.D. students and young specialists of higher educational institutions in the specialties of physics, nuclear physics and astronomy.
References
1 A.A. Detlaf, B.M. Yavorsky, L.B. Milkovskaya, Physics course. Vol. 2. Electricity and Magnetism (4th edition), (Moscow, Higher School, 1977), 384 p. (in Rus).
2 L.D. Landau, E.M. Lifshits, Short course in theoretical physics, Vol. 1: Mechanics. Electrodynamics, (Moscow, Science, 1969), 271 p. (in Rus).
3 A.N. Matveev, Electrodynamics, (2nd ed.), (Moscow, Higher. school, 1980), 383 p. (in Rus).
4 I.V. Saveliev The course of general physics, Vol. 2. Electricity, (Moscow, Science, 1970), - 442 p. (in Rus).
5 D.V. Sivukhin General course of physics, Vol. 3. Electricity (4th ed.), (Moscow, Fizmatlit; MIPT Publishing House, 2004), 656 p. (in Rus).
6 Ya.P. Terletsky, Yu.P. Rybakov, Electrodynamics. (2nd ed.), (Moscow, Higher. School, 1990), 352 p. (in Rus).
7 E. Purcell Berkleev's physics course. Vol. 2. Electricity and magnetism, (Moscow, Science, 1971), 448 p. (in Rus).
8 Ya.B. Zeldovich, I.D. Novikov, The theory of stars and the evolution of stars, (Moscow, Science, 1971), 486 p. (in Rus).
9 S. Shapiro, S. Tiukolski Black holes, white dwarfs and neutron stars, Trans. from English by ed. Ya. A. Smorodinsky, Vols 1-2, (Moscow, Mir, 1985), - 656 s. (in Rus).
10 Grechko L.G., Sugakov V.I., Tomasevich OF.F., Fedorchenko A.M. Collection of problems in theoretical physics,
(Moscow, Higher School, 1984), 319 p. (in Rus).
11 Griffiths, David J. Introduction to Electrodynamics, (5th ed.), (Pearson, 2017. ISBN 978-1108420419), 599 p.
12 James S. Marsh, American Journal of Physics, 50 (1), 51-53 (1982).
13 L.D. Landau, E.M. Lifshits, Theoretical Physics, Vol. II. Field theory. (8th ed.), (Moscow, Higher School, 2012), 536 p. (in Rus).
14 A.N. Tikhonov, A.A. Samara Equations of mathematical physics, (Moscow, Higher School, 2004), 798 p.
15 M. Abramowitz, I.A. Stegun Handbook of Mathematical Functions, (Dover Publications, Inc. New York, NY, USA © 1974 ISBN 0486612724, 1974), 1047 p.
16 J.D. Jackson, Classical Electrodynamics (3rd ed.), (New York: John Wiley & Sons. ISBN 978-0-471-30932-1. OCLC
925677836, 1999), 808 p.
17 W. Greiner, Classical Electrodynamics (Springer, New York, USA, 1998). - 566 p.
18 V.G. Boltyanskii, N.Ya. Vilenkin, Symmetry in algebra, (2nd ed.), (Moscow, MTSNMO, 2002), 240 p. (in Rus).
19 N.E. Kochin, Vector calculus and the beginnings of tensor calculus (9th ed.), (Moscow, Science, 1965), 427 p. (in Rus).
20 K. Boshkayev, M. Rotondo, R. Ruffini, Int. Journal Mod. Phys. Con. Ser., 12, 58-67 (2012).
21 P. Haensel, A.Y. Potekhin, D.G. Yakovlev (Eds.). Neutron Stars 1: Equation of State and Structure, (Astrophysics and Space Science Library, 2007), 326 p.
22 R. Belvedere, K. Boshkayev, J.A. Rueda, R. Ruffini, Nuclear Physics A, 921, 33-59 (2014).
23 N. Stergioulas, Living. Rev., 6, 174 (2003). https://arxiv.org/pdf/1612.03050.pdf
24 Software package “Wolfram Mathematica”: https://www.wolfram.com/mathematica/
25 R.L. Zimmerman, F.I. Olness, Mathematica for physics, (Copyright © 2002 by Addison-Wesley Publishing Company, Inc.), 665 p.
26 Sadri Hassani, Mathematical Methods Using Mathematica: For Students of Physics and Related Fields, 2003, 253 p.
2 L.D. Landau, E.M. Lifshits, Short course in theoretical physics, Vol. 1: Mechanics. Electrodynamics, (Moscow, Science, 1969), 271 p. (in Rus).
3 A.N. Matveev, Electrodynamics, (2nd ed.), (Moscow, Higher. school, 1980), 383 p. (in Rus).
4 I.V. Saveliev The course of general physics, Vol. 2. Electricity, (Moscow, Science, 1970), - 442 p. (in Rus).
5 D.V. Sivukhin General course of physics, Vol. 3. Electricity (4th ed.), (Moscow, Fizmatlit; MIPT Publishing House, 2004), 656 p. (in Rus).
6 Ya.P. Terletsky, Yu.P. Rybakov, Electrodynamics. (2nd ed.), (Moscow, Higher. School, 1990), 352 p. (in Rus).
7 E. Purcell Berkleev's physics course. Vol. 2. Electricity and magnetism, (Moscow, Science, 1971), 448 p. (in Rus).
8 Ya.B. Zeldovich, I.D. Novikov, The theory of stars and the evolution of stars, (Moscow, Science, 1971), 486 p. (in Rus).
9 S. Shapiro, S. Tiukolski Black holes, white dwarfs and neutron stars, Trans. from English by ed. Ya. A. Smorodinsky, Vols 1-2, (Moscow, Mir, 1985), - 656 s. (in Rus).
10 Grechko L.G., Sugakov V.I., Tomasevich OF.F., Fedorchenko A.M. Collection of problems in theoretical physics,
(Moscow, Higher School, 1984), 319 p. (in Rus).
11 Griffiths, David J. Introduction to Electrodynamics, (5th ed.), (Pearson, 2017. ISBN 978-1108420419), 599 p.
12 James S. Marsh, American Journal of Physics, 50 (1), 51-53 (1982).
13 L.D. Landau, E.M. Lifshits, Theoretical Physics, Vol. II. Field theory. (8th ed.), (Moscow, Higher School, 2012), 536 p. (in Rus).
14 A.N. Tikhonov, A.A. Samara Equations of mathematical physics, (Moscow, Higher School, 2004), 798 p.
15 M. Abramowitz, I.A. Stegun Handbook of Mathematical Functions, (Dover Publications, Inc. New York, NY, USA © 1974 ISBN 0486612724, 1974), 1047 p.
16 J.D. Jackson, Classical Electrodynamics (3rd ed.), (New York: John Wiley & Sons. ISBN 978-0-471-30932-1. OCLC
925677836, 1999), 808 p.
17 W. Greiner, Classical Electrodynamics (Springer, New York, USA, 1998). - 566 p.
18 V.G. Boltyanskii, N.Ya. Vilenkin, Symmetry in algebra, (2nd ed.), (Moscow, MTSNMO, 2002), 240 p. (in Rus).
19 N.E. Kochin, Vector calculus and the beginnings of tensor calculus (9th ed.), (Moscow, Science, 1965), 427 p. (in Rus).
20 K. Boshkayev, M. Rotondo, R. Ruffini, Int. Journal Mod. Phys. Con. Ser., 12, 58-67 (2012).
21 P. Haensel, A.Y. Potekhin, D.G. Yakovlev (Eds.). Neutron Stars 1: Equation of State and Structure, (Astrophysics and Space Science Library, 2007), 326 p.
22 R. Belvedere, K. Boshkayev, J.A. Rueda, R. Ruffini, Nuclear Physics A, 921, 33-59 (2014).
23 N. Stergioulas, Living. Rev., 6, 174 (2003). https://arxiv.org/pdf/1612.03050.pdf
24 Software package “Wolfram Mathematica”: https://www.wolfram.com/mathematica/
25 R.L. Zimmerman, F.I. Olness, Mathematica for physics, (Copyright © 2002 by Addison-Wesley Publishing Company, Inc.), 665 p.
26 Sadri Hassani, Mathematical Methods Using Mathematica: For Students of Physics and Related Fields, 2003, 253 p.
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How to Cite
Beisenov, B., Boshkayev, K., Brisheva, Z., Zhami, B., Kalymova, Z., Kuanyshbayuly, E., & Urazalina, A. (2019). Methods for calculating the magnetic field of rotating charge distribution with spherical symmetry. Recent Contributions to Physics (Rec.Contr.Phys.), 70(3), 82–91. https://doi.org/10.26577/RCPh-2019-i3-10
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Methods of teaching high school physics
