圆线圈平面磁场分布及其电感的计算与分析研究  

Calculation and analysis of plane magnetic field distribution and inductance of circular coil

作　　者：张克生 Zhang Kesheng(Teaching Department of Basic Courses,Jiangsu College of Safety Technology,Xuzhou 221011,China)

机构地区：[1]江苏安全技术职业学院基础课教学部,江苏徐州221011

出　　处：《江苏科技信息》2022年第24期45-49,共5页Jiangsu Science and Technology Information

摘　　要：对于圆形截面的载流圆线圈,当截面半径a远小于平均半径R时,用无限长直圆柱导体模型计算圆线圈内部的磁场,用线电流模型计算圆线圈外部的磁场,得到其所在平面的磁场分布表达式。文章通过数值积分计算,结果表明,当a/R<0.015时,圆线圈内、外侧面边界处两种模型计算的磁场值非常接近,边界处磁场近似连续变化。利用磁阻传感器实际测量了圆线圈平面的磁场分布,实验结果与计算值十分吻合。根据圆线圈平面磁场分布和诺依曼公式,得到圆线圈电感系数L的积分表达式,对比分析电感系数的3种计算方法,结果表明,当a/R<0.015时,L与R近似成正比,并随a增大而减小。两种数值积分计算的电感系数结果相等,与近似公式计算的误差随着线圈几何尺寸的增加而增大。For the current carrying circular coil with circular section,when the section radius a is far less than the average radius R,the magnetic field inside the circular coil is calculated by using the infinite straight cylindrical conductor model,and the magnetic field outside the circular coil is calculated by using the line current model,and the expression of the magnetic field distribution on the plane is obtained.When a/R<0.015,the numerical integration results show that the magnetic field values calculated by the two models at the inner and outer boundaries of the circular coil are very close,and the magnetic field at the boundary changes approximately continuously.The magnetic field distribution on the plane of circular coil is measured by magnetoresistive sensor,and the experimental results are in good agreement with the calculated values.According to the plane magnetic field distribution of circular coil and Neumann formula,the integral expression of circular coil inductance coefficient L is obtained.The three calculation methods of inductance coefficient are compared and analyzed.When a/R<0.015,the results show that L is approximately proportional to R and decreases with the increase of a.The results of inductance coefficient calculated by the two numerical integration are equal,and the error calculated by the approximate formula increases with the increase of coil geometric size.

关 键 词：磁场分布 数值计算 毕奥-萨伐尔定律 电感系数 诺依曼公式 

分 类 号：O441[理学—电磁学] TM551[理学—物理]