Secondly , some recently research results and some unsolved problems about the magnetic vector potential a , electric scalar potential and magnetic scalar potential of the transient eddy current formulation are deeply analyzed in the paper and the magnetic vector potential a is chosen to calculate the specified physical model discussed in this paper 其次,概括地分析了国内外对向量磁位( ? ) 、标量电位、标量磁位的研究现状及存在的问题,在此基础上,确定用向量磁位( ? )来计算永磁操动机构的物理模型,并证明在二维非线性情况下,库仑规范自然满足。
Firstly , in spherical coordinate system , the sovp formulation for the time - harmonic electromagnetic fields of the current dipole in conductive infinite - space is derived , using reciprocity theorem and transforming relations between special functions . then , selecting appropriate coordinate system , using superposition principle , the boundary - value problem of modified magnetic vector potential on the problem of a time - harmonic current dipole in spherical conductor is solved and analytical solution is obtained . finally , by means of the addition formulas of legendre polynomial and spherical harmonics function of degree n and order 1 , the analytical solution in spherical coordinate system specially located is transformed into that in spherical coordinate system arbitrarily located 首先利用特殊函数间的转化关系和互易定理推导得到了无限大导体空间中球坐标下时谐电流元电磁场的二阶矢量位形式:然后利用叠加原理,选择合适坐标系,求解了导体球中时谐电流元的修正磁矢量位边值问题,得到了问题的解析解;最后依据不同坐标系下电磁场解的转化原理,借助勒让德多项式和n次1阶球谐函数的加法公式,将坐标系特殊安放时的电磁场解析解变换到坐标系一般安放时的解析解,给出了球内电场和球外磁场的并矢格林函数。
The addition formula of spherical harmonics function of degree n and order 1 is derived using the relations between coordinate varieties after coordinate rotating and the property of the associated legendre polynomial . the relations among the magnetic vector potential , the modified magnetic vector potential and the second - order vector potential ( sovp ) are shown going forward one by one . it is explained that the solutions of electromagnetic fields in different coordinate systems can be transformed and an example having analytical solution is given 利用坐标旋转后球坐标变量间的关系和连带勒让德多项式的性质推导得到了n次1阶球谐函数的加法公式;以递进的方式说明磁矢量位、修正磁矢量位与二阶矢量位的关系,写出了引入二阶矢量位的过程;以时谐场矢量边值问题为例,阐明了不同坐标系下电磁场解的相互转化原理,给出了一个解析解的转化例子;在球坐标下,引入了较球矢量波函数更普遍的两类矢量函数,给出了其在球面上的正交关系。
Through the analyses of electromagnetic system of configuration of hollow metal cylinder by electromagnetic vector potential , an eddy current field math model is built by triangle cell , this article has researched power frequency to eddy current density , permeation depth and the effect of skin effect 文中通过对一个空心金属圆筒结构的电磁系统进行分析,以电磁场矢量位有限元法为基础对磁场强度、涡流密度进行了计算求解,采用三角形单元建立了涡流场数学模型,研究了电源频率对涡流密度、透入深度及集肤效应等场量的作用影响。
Adopting the assummation that the quark interaction is the sum of the usual one - gluon direct exchange and the mixture of linear scalar and vector potentials , we structure the relativistic corrections of order v2 / c2to the cornell potential , including the annihilation potential for the quark and antiquark of the same favors which plays the same role with the one - gluon direct exchange at short distances . the effects of the relativistic corrections on the hyperfine splittings of quarkonium states are discussed , and a good fit to the available experimental data is obtained on heavy quarkonium mass spectra 采纳库仑势源于单胶子直接交换,而线性禁闭源于标量和矢量的混合,同时考虑在短程区域与单胶子直接交换起同样作用的同味正反夸克的湮灭,构造了静态夸克-反夸克势到v ~ 2 c ~ 2级次的完全相对论修正,并拟合计算了重介子偶素的能谱,讨论了相对论修正对重介子偶素能级分裂的作用。
In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar field whose gradient is a given vector field.