轴对称电流的矢势和磁场
Vector Potential and Magnetic Field of Axially Symmetric Currents
摘要：
本文提出了一种求解任意轴对称电流分布的矢势和磁场的方法。在这种方法中，磁场和矢势不是通过求解微分方程而是通过直接计算一个标量函数的积分来寻找的。该解用相关联的勒让德多项式P_{lm}表示，其中勒让德多项式的指数m仅假设一个值，m = 1。解具有级数的形式，多项式的系数是多极矩的组合。关键词：电动力学，矢势，球谐函数，勒让德多项式，磁场。
英文摘要：
A solution is proposed for finding the vector potential and magnetic field of any distribution of currents with axial symmetry. In this approach, the magnetic field and the vector potential are looked for not by solving a differential equation but rather through straightforward calculation of integrals of one scalar function. The solution is expressed in terms of the associated Legendre polynomials P_{lm} with the index m of the Legendre polynomials assuming one value only, m = 1. The solution has the form of a series, with the coefficients of the polynomials being combinations of multipole moments. Key words: electrodynamics, vector potential, spherical harmonics, Legendre polynomials, magnetic field.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
