Beyond the Wires: How the Poynting Vector Reveals True Paths of Electromagnetic Energy - Yuan, Qidi (Transactions on Computer Science and Intelligent Systems Research, 2025)
The Poynting vector provides a rigorous framework for understanding electromagnetic energy flow, revealing that power is transported by fields in space rather than conductors. Although central to Maxwell’s equations, its physical interpretation in everyday circuits is often overlooked. This paper revisits the Poynting vector’s theoretical basis—energy density, Poynting’s theorem, and applicability in static and dynamic regimes—and applies it to three representative systems: a battery–resistor circuit, a coaxial cable, and a circular loop. Using a field-based analytical approach supported by peer-reviewed studies, each case demonstrates how electric and magnetic field configurations govern the paths of energy transfer. Calculations and visualizations confirm that the total Poynting flux matches conventional circuit-theoretic power, while exposing the spatial structure of energy distribution that circuit models cannot capture. The findings highlight the Poynting vector’s value as both a conceptual and practical tool. Clarifying fundamental misconceptions, informing high-frequency circuit design, and improving electromagnetic system analysis.