Degree Name
Master of Science
Graduate Program
Mathematics
Advisor
Omar Ghada
Abstract
There is a topological structure in the set of the electromagnetic field. The electromagnetic field boundary-value problems are obtained as solutions to Maxwell’s equations, which are first-order partial differential equations. This study will verify Maxwell’s equations in vacuum and have topological solutions characterized by the corresponding Hopf index n. Besides, this work will use the topological structure given by a scalar field, which represents a map S 3 × R → S 2 and determines the electromagnetic field through a certain transformation. We will show that the topological structure of the electromagnetic field is due to Maxwell’s divergence conditions.
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