Extension of Maxwell's equations for non-stationary magnetic fluids using gauss's divergence theorem

• The paper focuses on the development of non-stationary Maxwell's equations using Gauss's divergence theorem. • It is suggested that Gauss's divergence theorem be used to improve the numerical analysis of these generalized equations, which would make them more useful in magnetic fluid dynamics. • The paper examines the intricate interactions between non-conductive particles and conductive fluids under magnetic fields. • They could enable the development of more advanced electromagnetic devices and systems. • Creating a strong set of analytical tools that can find new scientific paths and useful applications is the main goal of the study, especially in the areas of electromagnetic induction and fluid dynamics. The work presented in this paper focuses on formulating the development of time-dependent electromagnetic field laws through the application of Gauss's divergence theorem. The first part of the discussion looks at the basic ideas of electromagnetism. It focuses on how classical formulations of the laws of electromagnetism can be adapted to account for non-stationary conditions, especially regarding magnetic fluids that don't conduct electricity. It is suggested that employing Gauss's divergence theorem could help improve the computational analysis of these generalized equations, which would make them more useful in magnetic fluid dynamics. The paper examines the intricate interactions between non-conductive particles and conductive fluids under magnetic fields. By putting these interactions into a single theoretical framework, this work aims to help us understand non-stationary electromagnetic phenomena and how they affect many different scientific and engineering fields. The concluding section of the study examines the prospective practical applications of these extended equations. They could enable the development of more advanced electromagnetic devices and systems. Creating a strong set of analytical tools that can find new scientific paths and useful applications is the main goal of the study, particularly in the areas of electromagnetic induction and fluid dynamics. This research offers potential for substantial progress in both theoretical comprehension and technological advancement, The proposed method is applicable to real-world systems such as ferrofluid-based cooling, magnetic dampers, plasma generators, and smart electromagnetic devices. These applications demonstrate the practical benefits of coupling field behavior with boundary dynamics using Gauss’s theorem.