摘要
从电流元相互作用能量的观念出发,推导出椭球形密绕线圈自感系数的积分表达式.利用Mathematica 10.3杰出的符号运算和数值计算能力、卓越的数字绘图功能,先把对方位角φ的积分结果表达为第一类和第二类完全椭圆积分的线性组合,进而对自感系数进行数值研究.计算并讨论了自感系数随椭球形线圈几何形状(c/a)的变化关系,结果表明:当c/a=1.7时单位体积的自感系数最小.最后给出了方便实用的自感系数多项式插值函数.
Based on the viewpoint of interaction energy of the current element, the integral expression of the self-inductance for a tightly wound ellipsoidal coil is derived. By using mathematica 10.3, the integral result for the azimuth angle ? is expressed as the linear combination of the first and the second kinds of complete elliptic integral, and then the self-inductance is numerically investigated. The axis ratio ( c/a ) dependence of the self-inductance is calculated and discussed. This result shows that when c/a =1.7, the self-inductance per unit volume is the minimum . Finally, a convenient and practical polynomial interpolation function for self-inductance is given.
作者
江俊勤
JIANG Jun-qin(Department of Physics and Information Engineering, Guangdong University of Education, Guangzhou,Guangdong 510303, China)
出处
《大学物理》
2019年第5期20-23,56,共5页
College Physics
基金
广东省高等学校专业综合改革试点项目(XM060012物理学)资助
关键词
椭球形线圈
自感系数
椭圆积分
数值分析
多项式插值函数
ellipsoidal coil
self-inductance
Elliptic integral
numerical analysis
polynomial interpolation function
