Abstract
This article analyzes and discusses the extended theory of Gauss's law and its potential applications in different fields. In the theoretical foundation section, the article elaborates on the definition, theory, and formulas of the traditional Gauss's law, providing mathematical derivations. Additionally, it reviews the applications of Gauss's law in electrostatics and gravitational fields, including aspects such as electric field flux, electric potential displacement, gravitational field, and mass distribution. In the potential application analysis section, the article explores the potential applications of Gauss's law in fields such as communications, acoustics, and medicine The expanded theories and potential applications of Gauss's theorem provide us with a unified mathematical framework at the macroscopic level for describing and explaining physical phenomena in different fields. By applying Gauss's theorem and its extended forms, we can better understand and explore various phenomena in the natural world, applying them to acoustics, medicine, and scientific research, thus advancing technological development and addressing practical problems.
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