## 6 Conclusions  
This article develops the fundamental works of [PERSON] [PERSON] [3], [PERSON], and others [4], in which the solution to the problem of the field of a horizontal dipole placed over a semi-conducting medium using the Fourier-Bessel integral transformation is given. Moreover, the problem solved in this article is not identical to the original problem of the horizontal dipole field. Our emitter is a grounded cable of finite length, the field of which is investigated in the work of the first author of the article [PERSON] [2]. The field of this emitter at distances greater than \(3b\) can be represented as the sum of the fields of two-point antiphase-powered sources. This fact made it possible to represent the field in  
Figure 5: The flow characteristic:(**a**)—corresponds to the free space for \(H=\infty\), \(h=\)3 m; (**b**)—the flow characteristic for \(H\)=6 m, \(h=\) 3 m.  
Figure 6: The flow characteristic: (**a**)—corresponds to the free spacefor \(H=\)\(\infty\), \(h=\)1.5 m; (**b**)—the flow characteristic \(H\)=6 m, for \(h=\) 4.5 m.  
the conducting layer with a scalar potential \(U\), which significantly reduced the amount of calculations. To determine the diffraction field of an elongated dielectric spheroid, an exact solution was taken in a homogeneous field at a constant current of J. [PERSON] (2018), which was decomposed into a Taylor series. The first dipole term of the series is represented by an alternating current. As a result, the resulting diffraction field was obtained in the form of equivalent fields of horizontal and vertical dipoles. To determine the field in the conducting layer, we used some ideas of [PERSON], [PERSON] (2018), who studied electromagnetic and acoustic fields in layered media. This article proves that the bottom practically does not affect the field in the conductive layer, and the water-air boundary provides a mirror image of the fields of the vertical and horizontal dipoles of the spheroid and the field of the grounded cable.  
Such a solution in elementary functions was obtained for the first time by the original method. As an example, the diffraction field of an elongated dielectric spheroid in a conducting layer excited by the field of a transmitting EA is calculated (Figure 1). As a result, a good agreement of the theoretical calculations with the results of the experimental data obtained from a life-size model of a security device on the sea shelf of the Gulf of Finland was achieved. We believe that active water area security systems using linear electrode antennas are more promising than acoustic security systems in shallow water at a \(H\) of up to 10 m.  
Thus, the developed mathematical model makes it possible to calculate the flow characteristics of conductive and non-conductive bodies in the water with sufficient accuracy for practice, which allows digital filtering of the received signal and significantly increases the signal-to-noise ratio and the detection range of the object. This is the theoretical basis for the creation of various security systems in rivers, canals, and on the sea shelf. This article was prepared as part of the Mining University publication plan for 2022.  
Y.K. Belongs to the conceptualization of the original research method and methodology for the development of a mathematical model for solving the problem with a formal analysis of the results, as well as the preparation of the manuscript; S.P. owns the software, calculations, review and editing, visualization and discussion of the results of the work. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available in the article. Initial experimental data are available on request from the corresponding author.  
The authors declare no conflict of interest.