Application of Schwartz Christoffel Transformation as a Conformal Map in Solving Some Physical Problems

Ismaila Omeiza Ibrahim¹ , Manjak Nibron Haggai² , Kwami Adamu Mohammed³

Section:Research Paper, Product Type: Journal-Paper
Vol.12 , Issue.2 , pp.47-54, Apr-2024

Online published on Apr 30, 2024

Copyright © Ismaila Omeiza Ibrahim, Manjak Nibron Haggai, Kwami Adamu Mohammed . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
This research work was purely on conformal mapping method. Existence of Schwarz-Christoffel transformation was briefly discussed and a lightning conductor was modelled as an illustration by the boundary-value problem in which the potential u is equal to zero at x = 0 which satisfies Laplace’s equation in the half-space x > 0 and u to be bounded at infinity and the solution is bounded at . Another illustration which showed, the cross section of two metallic conductors the lower conductor is of infinite extent which lies on the real axis and at infinity . The other conductor is semi-infinite in length and extends from . We also find the streamlines and equipotentials for this situation and obtained the voltage everywhere in space and we plot the equipotentials and electric flux lines, in which the charge tends to be concentrated at the edge of the upper plate. Furthermore, all the results were visualized with the aid of MATLAB, electric field is then directed downward, from the higher to the lower potential, and has magnitude equal to the voltage difference between the plates.

Key-Words / Index Term :
conformal map, Schwarz-Christoffel transformation, Boundary value problem, laplace equation, stream lines, equipotentials, electric flux lines, lightning conductor.

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