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Abstract

This paper examines the role of conformal transformations and their derivatives in the analysis of electric potential distribution with boundary conditions in complex regions on the plane. The importance of these transformations lies in preserving the fundamental properties of the domain and enabling the conversion of complex geometries into simpler forms, which facilitates the mathematical solution process and the attainment of precise answers. In this study, using mathematical analysis methods and conformal transformations, complex physical regions are transformed into simpler domains such as the unit disk or the upper half-plane, and electric potential distributions are solved in these simpler regions. The results are then mapped back to the original domains. The findings demonstrate that conformal transformations are an effective tool in analyzing electrostatic problems in complex regions. Finally, three practical examples of these transformations are presented.

Keywords

Conformal Mapping Electric Potential Distribution Boundary Conditions Complex

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Noori, M. Z., Haidary, M. K., Noori, N., & Baidar, A. W. (2026). Application of Conformal Mapping and Its Derivative in Electric Potential Distribution. Journal of Natural Sciences – Kabul University, 8(4), 149–175. https://doi.org/10.62810/jns.v8i4.455
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