## Abstract

The paper deals with the capacitance of cylindrical two-dimensional capacitor which consists of Cartesian orthotropic dielectric material. The determination of the capacitance of capacitor with orthotropic dielectric material by a suitable coordinate transformation is reduced to the computation of capacitance of an isotropic capacitor. It is proven that the capacitance of a Cartesian orthotropic capacitor can be obtained in terms of an isotropic capacitor whose dielectric constant is the geometric mean of the dielectric constant of the orthotropic capacitor.

## 1 Introduction

Combining different computation methods with analytical procedures is a common method for solving electrical problems. Paper [1] developes a computation method determining eddy currents effect in electrical steel sheets. Ecsedi and Baksa formulate a mathematical model to obtain upper and lower bounds for a three-dimensional hollow non-homogeneous body [2].

This study includes the determination of a cylindrical two-dimensional capacitor. The considered capacitor consists of homogeneous and orthotropic dielectric materials. The capacitance is the ability of a capacitor to store electric charge per unit voltage across its inner and outer surfaces. The capacitance is a function depending on the geometry of a capacitor and the permittivity of its dielectric material. The solution of the capacitance of capacitor with Cartesian orthotropic dielectric materials is reduced to the problem of capacitor with isotropic dielectric material with a suitable homogeneous linear coordinate transformation. Knowledge of electricity, which is necessary for formulating and solving the set task, can be found in detail in books [3–6]. This type of the presented approach was used in paper [7] to solve the Saint-Venant's torsion problem of Cartesian orthotropic elastic bars.

## 2 Governing equations of electrostatic field for two-dimensional capacitor

It must be noted that the capacitance of a capacitor of width

## 3 Transformation of the governing boundary value problem

Two-dimensional hollow plane domain in the plane

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

Two-dimensional hollow plane domain in the plane

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

Two-dimensional hollow plane domain in the plane

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

## 4 Determination of the capacitance of anisotropic capacitor

## 5 Example

Isotropic two-dimensional capacitor with cylindrical boundary curves

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

Isotropic two-dimensional capacitor with cylindrical boundary curves

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Isotropic two-dimensional capacitor with cylindrical boundary curves

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

Anisotropic two-dimensional capacitor with elliptical boundary curves

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

Anisotropic two-dimensional capacitor with elliptical boundary curves

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

Anisotropic two-dimensional capacitor with elliptical boundary curves

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

The graphs of ^{−1)}, ^{−1)},

The graph of

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

The graph of

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

The graph of

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

The graph of

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

The graph of

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

The graph of

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

The contour lines of the function

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

The contour lines of the function

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

The contour lines of the function

Citation: Pollack Periodica 2023; 10.1556/606.2023.00828

## 6 Conclusions

The considered two-dimensional cylindrical capacitor consists of homogeneous Cartesian orthotropic dielectric material. The capacitance of orthotropic capacitor is expressed in terms of a homogeneous capacitor whose permittivity is the geometrical mean of the principle values of the Cartesian orthotropic capacitor.

## References

- [1]↑
J. Pippuri and A. Arkkio, “2D – 1D time–harmonic model for rotating electrical machines,”

, vol. 1, no. 3, pp. 79–90, 2006.*Pollack Period.* - [2]↑
I. Ecsedi and A. Baksa, “Bounds for the electrical resistance for non-homogeneous conducting body,”

, vol. 18, no. 1, pp. 172–176, 2023.*Pollack Period.* - [3]↑
K. Simonyi,

. Oxford: Pergamon Press, 2016.*Foundations of Electrical Engineering: Fields – Networks – Waves* - [4]
E. M. Purcell and D. J. Morin,

. Cambridge: Cambridge University Press, 2013.*Electricity and Magnetism* - [5]
R. E. Thomas, A. J. Rosa, and G. J. Toussaint,

. New York: Wiley, 2023.*The Analysis and Design of Linear Circuits* - [6]
A. K. Raychaudhuri,

. Berlin: Springer, 2022.*Classical Theory of Elecricity and Magnetism* - [7]↑
I. Ecsedi and A. Baksa, “A method for the solution of uniform torsion of Cartesian orthotropic bar,”

, vol. 52, pp. 129–143, 2022.*J. Theor. Appl. Mech.*