DETERMINATION OF THE CHARACTERISTICS OF THE ELECTROSTATIC FIELD OF CAPACITORS USING AN ANALYTICAL FUNCTION

The theory of analytical functions is widely used not only in fundamental research. It is a universal tool that allows you to formalize physical phenomena, facilitate the analysis of complex systems, solve complex physical problems, increasing the accuracy and efficiency of the results. With the help of analytical functions, many problems are reduced to simpler formulas that are easily interpreted. It also becomes possible to obtain analytical solutions without numerical methods, and the Cauchy-Riemann equations allow you to simultaneously describe several physical characteristics. In particular, in electrodynamics and field theory, analytical functions are used to describe potentials and fields, and the conformal mappings they perform are used to determine the distribution of the electric field in complex geometric regions, for example, around an electrode in the form of a corner or near sharp edges. In this article, an analytical function called the complex potential is used to determine the characteristics of the electrostatic field of flat and cylindrical capacitors. In particular, by studying the complex potential of the electrostatic field of flat and cylindrical capacitors, families of equipotentials and flux lines were obtained for them, the direction of the electrostatic field strength vector E was determined, and the capacitance C was calculated for these types of capacitors. It is indicated that the electrostatic field strength vector E of a flat capacitor is constant and directed normal to the surface of the capacitor plates, and in the case of a cylindrical capacitor, the vectors E and D (electrostatic induction vector) are directed radially from the inner cylinder (r = a) to the outer (r = b), if the inner one has a positive charge).