疏绕椭球形线圈磁场的空间分布

Spatial Distribution of Magnetic Field from Sparse Winding Ellipsoidal Coil

从毕奥-萨伐尔定律出发,先推导出疏绕在旋转椭球面上载流线圈磁场的积分计算式,然后用数值分析的方法研究磁场的空间分布.利用Mathematica9.0强大的计算能力、卓越的数字绘图功能绘制了磁场的三维分布图.结果直观地表明:当椭球形状一定时,中心的磁感应强度与单位长度匝数n成正比,而且匝数越多均匀区域就越大;当单位长度匝数n一定时,长短轴的比值越大、中心区内磁场就越强.

Based on the Biot-Savart law. the integral expression of the magnetic field from a current carrying sparse winding rotation ellipsoidal coil is derived, the spatial distribution of this magnetic field is nunlerically studied. By using the famous software MATHEMATICA 9.0. the three-dimensional maps of the distribution of magnetic field are plotted. The results show： When the ellipsoid shape is fixed. the magnetic induction intensity in the central area is proportional to the number of turns per unit length of the coil. The more the number of turns per unit length is, the wider the central uniform area is. when the ,tumber of turns per unil length is certain, the bigger the ratio of long axis and short axis is. the stronger the magnetic field is.