Dimensional Analysis via an Electromagnetically-Oriented Set of Fundamental Dimensions

Abstract

Abstract. This paper describes the electromagnetically-oriented  dimensional basis that is based on the reference dimensions of Length ( ), Time (T), Electric Current ( ), and Electric Potential ( ). We utilize this basis in the matrix solution of dimensional-analysis (DA) problems involving mainly electromagnetic quantities. Representations of electromagnetic quantities in the  basis (compared with the standard  basis that uses Mass ( ) instead of Potential ( )) are more informative, much simpler, and have salient duality features. Moreover, DA computations of electromagnetic problems via the Gauss-Jordan algorithm in the  basis are more efficient, much less error prone, and quicker to detect linear dependencies in the dimensional equations. Both details and advantages of the proposed method are explored via demonstrative examples, which are of obvious significance in the learning and teaching of electromagnetism.