Magnetic field and inductance of filament conductor segment model with current continuity

Traditional current-carrying model of filament conductor segment is the basic model for analyzing the magnetic field in a closed conductor loop. Although it does not satisfy the law of current continuity, it is still suitable for analyzing the magnetic field in the closed conductor loop. However, for the current distribution problem of some local multi-branch parallel-connection conductor segments in a closed conductor loop, the traditional model cannot fully reflect the interaction between magnetic fields of the local multi-branch parallel-connection conductor segments. For this reason, the displacement current model proposed in the existing literature satisfies the law of current continuity and solves the above problem well. But, there remain some problems to be solved, such as incomplete theory, inconsistency and complex formulae in the existing literature. In this paper, a conductive current-carrying model of filament conductor segment is proposed, which ensures current continuity inside, outside, and on two terminals of the filament conductor segment. The differential equation of total magnetic field with more profound physical connotation and the formulae of vector magnetic potential are derived in detail. Further, the formulae for calculating magnetic field energy and inductance of the conductive current-carrying model of filament conductor segment are proposed, which greatly reduces the computational complexity and makes up for the shortcoming of model in the existing literature. An example given in this paper verifies the correctness of the above theory and formulae.