I. P. Kovalyov1, N. I. Kuzikova2
1, 2 Nizhny Novgorod State Technical University n.a. R.E. Alekseev (Nizhny Novgorod, Russia)

1 physics@nntu.nnov.ru, 2 nata.kuz68@mail.ru

The article derives an equation for the electric field lines of a dipole, the dipole moment of which depends on time. It simplifies the graphical representation of fields compared to the method based on solving differential equations for electric field lines. To uniquely solve differential equations, initial conditions are required, which, as a rule, are not specified. When constructing field lines using the resulting equation, not only is there no need to solve differential equations, but there is also no need to calculate the field strength; it is enough to know only the law of change of the dipole moment with time.

The resulting equation has been used to construct the field lines that arise when a static dipole is turned on and when a harmonic dipole is turned on. Moreover, it has been assumed that the dipole moment does not change instantly, and the switching process takes a finite time. Then the nonstationary electric field also occupies a finite region of space, which makes it possible to examine in detail the structure of the nonstationary field.

The space occupied by the field that appears when a static dipole is turned on can be divided into two areas. This is a spherical region in the center of which there is a dipole. The field in this region is a static dipole field. The second region is a spherical layer located near the front of the emitted electromagnetic wave. The field in the layer is determined by the increasing dipole moment.

The electric field that appears when the harmonic dipole is turned on is divided into spherical layers. In each of the layers there are closed lines of force that do not affect the other layers. An expression for the number of layers and an equation for calculating the radii of spheres, which are the boundaries of spherical layers, are given.

Kovalyov I.P., Kuzikova N.I. Propagation of a non-stationary field when an electric dipole is turned on. Antennas. 2025. № 2. P. 14–21. DOI: https://doi.org/10.18127/j03209601-202502-02 (in Russian)

1. Gol'dshejn L.D., Zernov N.V. Elektromagnitnye polya i volny M.: Sov. radio. 1971. (in Russian)
2. Tamm I.E. Osnovy teorii elektrichestva. M.: Fizmatlit. 2003. (in Russian)
3. Nikol'skij V.V., Nikol'skaya T.I. Elektrodinamika i rasprostranenie radiovoln. M.: Nauka. 1989. (in Russian)
4. Nikol'skij V.V. Teoriya elektromagnitnogo polya. M.: Vysshaya shkola. 1961. (in Russian)
5. Topics in applied physics. V. 107. Transient electromagnetic fields. Ed. by L.B. Felsen. Berlin – New-York: Springer. 1976.
6. Astanin L.Yu., Kostylyov A.A. Osnovy sverkhshirokopolosnykh radiolokatsionnykh izmerenij. M.: Radio i svyaz'. 1989. (in Russian)
7. Podosenov S.A., Potapov A.A., Sokolov A.A. Impul'snaya elektrodinamika shirokopolosnykh radiosistem i polya svyazannykh struktur. Pod red. A.A. Potapova. M.: Radiotekhnika. 2003. (in Russian)
8. Baum C.E. Emerging technology for transient and broadband analysis and synthesis of antennas and scatterers. Proc. IEEE. 1976. V. 64. № 11. P. 1698–1717.
9. Bolotovskij B.M., Davydov V.A., Rok V.E. Ob izluchenii elektromagnitnykh voln pri mgnovennom izmenenii sostoyaniya izluchayushchej sistemy. UFN. 1978. T. 126. № 2. S. 311–321. (in Russian)
10. Gigoryan A.T., Vyal'tsev A.N. Genrikh Gerts. M.: Nauka. 1968. (in Russian)
11. Mohamed N.J. Lines of force for a Hertzian electric dipole. IEEE Transactions on Electromagnetic Compatibility. 1987. V. 29. № 3. P. 242–245.