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This research focuses on developing methods to identify and visualize electromagnetic coupling paths. The basis of the approach is to utilize an analogy between electromagnetic energy flow and fluid flow. This allows one to apply the theories and algorithms of fluid dynamics to electromagnetics and thereby to visualize the electromagnetic energy flow. This, in turn, can be utilized to identify the electromagnetic coupling path. In this paper (Part I of a two-part series), the basic idea of the method is introduced and the concepts of the electromagnetic energy parcel and its trajectory are explained. The characteristics of the instantaneous trajectory of an energy parcel will be explained in detail and illustrated with canonical examples. The applicability of the instantaneous trajectory of energy parcels in practical problems will be discussed. Part II will focus on the application of this method to solving practical electromagnetic compatibility problems. The utility of the concepts and methodology will be demonstrated using real-world applications.