圆锥曲线电流磁场分析  

Analysis of Magnetic Field for Conic Electric Current Based on Mathematica

作　　者：孙立红[1] 成泰民[1] 

机构地区：[1]沈阳化工大学数理系,辽宁沈阳110142

出　　处：《沈阳建筑大学学报（自然科学版）》2012年第4期765-768,共4页Journal of Shenyang Jianzhu University：Natural Science

基　　金：国家自然科学基金项目(10647138);辽宁省教育厅科学研究项目(20060667)

摘　　要：目的研究可以用于平面曲线电流的磁感应强度计算的方法.方法在稳恒电流条件下根据毕奥—萨伐尔定律,采用矢量分析的方法对直角坐标系中的载流直导线在原点处磁感应强度进行了推导,得到了通用解析式.对椭圆形线电流中心以及圆锥曲线电流焦点的磁场进行讨论,并进行了数值分析.结果当椭圆离心率e从0开始增大时,椭圆形线电流在中心(焦点)处的磁感应强度开始增大,当双曲线离心率e由1开始增大时,双曲线形线电流在其焦点处的磁感应强度大小也随之开始迅速减小,当椭圆(双曲线)离心率e→1时,椭圆形线(双曲线)电流在其焦点处磁感应强度B→∞.结论分析结果证明此方法具有通用性.An analytic method for magnetic induction intensity of plane curve electric current is found through magnetic induction intensity computation analysis of the current-carrying straight wire. Based on Bi- ot-Savart Law that steady current produces magnetic field, an analytic formulation was derivated under rec- tangular coordinates for current-carrying wire＇s origin magnetic induction intensity by using vector analysis. The magnetic induction intensity of elliptic electric current center and conic electric current＇s focus is dis- cussed by the analytic formulation. The numerical analysis shows that the magnetic induction intensity at the focus of elliptic current increases with the elliptical eccentricity＇s increasing from 0;the magnetic induction intensity at the focus of hyperbolic current decreases rapidly with the hyperbolic eccentricity＇s increasing from 1 ; the magnetic induction intensity at the focus of elliptic （hyperbolic） current approaches infinity when elliptic （hyperbolic）eccentricity approaches 1. Analyzed through Mathematica, the result proves this analytic method has certain versatility.

关 键 词：磁感应强度 圆锥曲线电流 毕奥—萨伐尔定律 电流元 焦点 

分 类 号：O441[理学—电磁学]