ISSN 1119-4618
 

Original Article 


ON THE APPLICATION OF CONFORMAL MAPS IN THE SOLUTION AND ANALYSIS OF SOME ELECTROSTATIC FIELDS

Swem Samuel Tarkar, Swem Doowuese Swem.

Abstract
In this paper, we have employed appropriate conformal maps to solve and analyze some harmonic Dirichlet problems in electrostatics. The technique involves the transformation of a given problem in the w plane onto one in the upper half of the z plane where it is identified as the imaginary part of the logarithmic function with branch cut at the ray -Ď€/2 and efficiently solved or directly solving it in the w plane where it is posed. The equipotential lines and flux lines of the electric field were also generated to show the nature of the field and the features of the solution. The method gave exact general analytical solutions in closed form to the problems considered and could therefore be a useful alternative method for solving Laplace’s equation for two dimensional electrostatic problems.

Key words: Domain, Region, Conformal Map, Joukowski Map, Bilinear Transformation, Analytic Function, Branch Cut and Branch of a Multiple Valued Function, Electrostatic Potential, Equipotential Lines, Flux Lines, Electric field Intensity.


 
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How to Cite this Article
Pubmed Style

Tarkar SS, Swem SD, . ON THE APPLICATION OF CONFORMAL MAPS IN THE SOLUTION AND ANALYSIS OF SOME ELECTROSTATIC FIELDS. JPAS. 2021; 21(1): 173-180. doi:10.5455/sf.114105


Web Style

Tarkar SS, Swem SD, . ON THE APPLICATION OF CONFORMAL MAPS IN THE SOLUTION AND ANALYSIS OF SOME ELECTROSTATIC FIELDS. http://www.atbuscienceforum.com/?mno=114105 [Access: May 11, 2021]. doi:10.5455/sf.114105


AMA (American Medical Association) Style

Tarkar SS, Swem SD, . ON THE APPLICATION OF CONFORMAL MAPS IN THE SOLUTION AND ANALYSIS OF SOME ELECTROSTATIC FIELDS. JPAS. 2021; 21(1): 173-180. doi:10.5455/sf.114105



Vancouver/ICMJE Style

Tarkar SS, Swem SD, . ON THE APPLICATION OF CONFORMAL MAPS IN THE SOLUTION AND ANALYSIS OF SOME ELECTROSTATIC FIELDS. JPAS. (2021), [cited May 11, 2021]; 21(1): 173-180. doi:10.5455/sf.114105



Harvard Style

Tarkar, S. S., Swem, S. D. & (2021) ON THE APPLICATION OF CONFORMAL MAPS IN THE SOLUTION AND ANALYSIS OF SOME ELECTROSTATIC FIELDS. JPAS, 21 (1), 173-180. doi:10.5455/sf.114105



Turabian Style

Tarkar, Swem Samuel, Swem Doowuese Swem, and . 2021. ON THE APPLICATION OF CONFORMAL MAPS IN THE SOLUTION AND ANALYSIS OF SOME ELECTROSTATIC FIELDS. Science Forum (Journal of Pure and Applied Sciences), 21 (1), 173-180. doi:10.5455/sf.114105



Chicago Style

Tarkar, Swem Samuel, Swem Doowuese Swem, and . "ON THE APPLICATION OF CONFORMAL MAPS IN THE SOLUTION AND ANALYSIS OF SOME ELECTROSTATIC FIELDS." Science Forum (Journal of Pure and Applied Sciences) 21 (2021), 173-180. doi:10.5455/sf.114105



MLA (The Modern Language Association) Style

Tarkar, Swem Samuel, Swem Doowuese Swem, and . "ON THE APPLICATION OF CONFORMAL MAPS IN THE SOLUTION AND ANALYSIS OF SOME ELECTROSTATIC FIELDS." Science Forum (Journal of Pure and Applied Sciences) 21.1 (2021), 173-180. Print. doi:10.5455/sf.114105



APA (American Psychological Association) Style

Tarkar, S. S., Swem, S. D. & (2021) ON THE APPLICATION OF CONFORMAL MAPS IN THE SOLUTION AND ANALYSIS OF SOME ELECTROSTATIC FIELDS. Science Forum (Journal of Pure and Applied Sciences), 21 (1), 173-180. doi:10.5455/sf.114105