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International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749


Matrix Dimensional Analysis for Electromagnetic Quantities

Matrix Dimensional Analysis for Electromagnetic Quantities

Mostafa Ali Rushdi
Faculty of Engineering and Technology, Future University in Egypt (FUE), New Cairo, 11835, Arab Republic of Egypt. (Currently with Interdisciplinary Graduate School of Engineering Sciences (IGSES), Earth System Science and Technology (ESST), Kyushu University, Fukuoka, 816-8580, Japan).

Ali Muhammad Rushdi
Department of Electrical and Computer Engineering, King Abdulaziz University Jeddah 21589, Kingdom of Saudi Arabia.

DOI https://doi.org/10.33889/IJMEMS.2021.6.2.039

Received on September 22, 2020
  ;
Accepted on January 02, 2021

Abstract

We utilize the electromagnetically-oriented LTI∅ dimensional basis in the matrix solution of dimensional-analysis (DA) problems involving mainly electromagnetic quantities, whether these quantities are lumped or distributed. Representations in the LTI∅ basis (compared with the standard MLTI basis) are more informative and much simpler. Moreover, matrix DA computations employing the LTI∅ basis are more efficient and much less error prone. Extensive discussions of two demonstrative examples expose technical details of a novel DA scheme, and clarify many important facets of modern dimensional analysis.

Keywords- Dimensional analysis, Gauss-Jordan algorithm, Bases and regimes, Electromagnetics, Duality, The LTI∅ basis, The MLTI basis.

Citation

Rushdi, M. A., & Rushdi, A. M. (2021). Matrix Dimensional Analysis for Electromagnetic Quantities. International Journal of Mathematical, Engineering and Management Sciences, 6(2), 636-644. https://doi.org/10.33889/IJMEMS.2021.6.2.039.

Conflict of Interest

The authors assert that no conflict of interest exists.

Acknowledgements

The authors are greatly indebted to Dr. Ahmad Ali Rushdi for the technical help he generously and proficiently offered during the preparation of this manuscript. They are really appreciative of his perseverance and his expertise.

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