Method for Solving Physical Problems Described by Linear Differential Equations

A method for solving physical problems is suggested in which the general solution of a differential equation in partial derivatives is written in the form of decomposition in spherical harmonics with indefinite coefficients. Values of these coefficients are determined from a comparison of the decomposition with a solution obtained for any simplest particular case of the examined problem. The efficiency of the method is demonstrated on an example of calculation of electromagnetic fields generated by a current-carrying circular wire. The formulas obtained can be used to analyze paths in the near-field magnetic (magnetically inductive) communication systems working in moderately conductive media, for example, in sea water.

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Correspondence to B. A. Belyaev.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 140–146, September, 2016.

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Belyaev, B.A., Tyurnev, V.V. Method for Solving Physical Problems Described by Linear Differential Equations. Russ Phys J 59, 1482–1490 (2017). https://doi.org/10.1007/s11182-017-0934-9

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Keywords

  • current-carrying coil
  • electromagnetic field
  • linear equations in partial derivatives
  • spherical harmonics
  • near-field magnetic communication