On the expanded Maxwell's equations for moving charged media system-General theory, mathematical solutions and applications in TENG

The conventional Maxwell's equations are for media whose boundaries and volumes are fixed. But for cases that involve moving media and time-dependent configuration, the equations have to be expanded. Here, starting from the integral form of the Maxwell's equations for general cases, we first derived the expanded Maxwell's equations in differential form by assuming that the medium is moving as a rigid translation object. Secondly, the expanded Maxwell's equations are further developed with including the polarization density term P-s in displacement vector owing to electrostatic charges on medium surfaces as produced by effect such as triboelectrification, based on which the first principle theory for the triboelectric nanogenerators (TENGs) is developed. The expanded equations are the most comprehensive governing equations including both electromagnetic interaction and power generation as well as their coupling. Thirdly, general approaches are presented for solving the expanded Maxwell's equations using vector and scalar potentials as well as perturbation theory, so that the scheme for numerical calculations is set. Finally, we investigated the conservation of energy as governed by the expanded Maxwell's equations, and derived the general approach for calculating the displacement current partial derivative/partial derivative t P-s for the output power of TENGs. The current theory is general and it may impact the electromagnetic wave generation and interaction (reflection) with moving train/car, flight jets, missiles, comet, and even galaxy stars if observed from earth.

Automated summary

This study derived the expanded Maxwell's equations for moving media and time-dependent configurations from the integral form of the equations. These expanded equations are the most comprehensive governing equations including both electromagnetic interaction and power generation. The study also developed a first principle theory for triboelectric nanogenerators based on these expanded equations. Additionally, general approaches for solving the expanded Maxwell's equations and calculating the displacement current for the output power of the nanogenerators were presented. The impact of this theory extends to electromagnetic wave generation and interaction with moving objects such as trains, cars, jets, missiles, comets, and galaxy stars if observed from earth.