Browsing by Author "Alruthaya, Ibtisam Sulaiman"

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Formulation of Maxwell's Equation in Terms of Quaternions
(Saudi Digital Library, 2021) Alruthaya, Ibtisam Sulaiman; Mohamed, Arbab Ibrahim Arbab
Quaternions are a mathematical description of a physical system that extends the complex numbers. They are comprehensively characterized and are highly capable of describing natural phenomena. Worth noting is that James C. Maxwell initially used it in formulating the electromagnetic theory in 1873, as it contained 20 equations that remained unresolved for 50 years until they were simplified and reduced to 4 famous equations by Heaviside and Gibbs resulting in the loss of many important terms for describing electromagnetic phenomena despite the importance of their efforts. The electromagnetic theory is one of the most reliable theories at present. It was originally formulated based on experiments and proven facts, and its applications are present in all fields, adding to it that it accepts reformulation. Nevertheless, it appears that there is a deficiency in the description of the electromagnetic theory as it failed to explain certain issues. The aim of this thesis is to generalize the electromagnetic theory. Here, Maxwell's equations are reformulated using quaternions and the missing terms are restored in a more straightforward way that differs from the principle that Maxwell worked on. Then the study of the equations is performed. The report explores their properties and the new quantities that emerged from the new formulation and compares the results with the previous work and then includes some phenomena associated with electromagnetism in the same manner, which will add more physical meanings and properties to the new formulation.
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