The Complex Vector Maxwell Equations and an Applied Research

Abstract

Different forms of Maxwell equations can clearly describe macroscopic electromagnetic laws of different problems. The complex vector Maxwell equations are deduced on the basis of the plural form equations. They visually show a process and a rule that a time-varying electromagnetic field is stimulated by a harmonic current source. Firstly, with reference to the complex vector Maxwell equations, the author analyzes basic rules and characteristics of the electromagnetic field that current source excites in the infinite conductive medium. It reveals an interdependent mechanism among the current, magnetic and electric field. Secondly, they are applied to the analysis of electromagnetic and current characteristics that a coil current source generates in induction logging around the borehole. The results show that the complex vector Maxwell equations not only clearly describe a physical relationship of mutual dependence and mutual excitation among the real vector and imaginary vector of the electric-field intensity, magnetic field intensity, induced current, displacement current and excitation current, but also deeply appears a relationship between the receiving voltage and the formation parameters in induction logging. The numerical calculation and drawing graphics display a law of the real vector and imaginary vector of the electric field intensity, magnetic field intensity, induced current, displacement current and excitation current.