矩形截面线圈稳恒磁场的积分算法

从Biot-Savart定律和矢量叠加原理出发,发展了一种计算矩形截面不规则线圈稳恒磁场的积分算法.根据线圈的形状,将直流电流分割成直线段电流元和曲线段电流元,采用多个直线段电流元来拟合曲线段电流元,并将所有直线段电流元的磁场三重积分形式分别转化为一重积分;最后进行数值求解.为了快速求解这些积分,分别推导了梯形棱柱体电流元、三角形棱柱体电流元和梯形面电流元的磁场积分方程.模型验证表明,计算值与理论值符合良好.

Integral Method to Calculate Magnetostatic Field Caused by Irregular Coil with Rectangular Section

Based on the Biot-Savart law and principle of vector superposition,an integral method was developed to calculate the magnetostatic field due to irregular coil of rectangular-section conductor.According to conductor shape,the DC coil is divided into two parts: straight-line current elements and curved current elements,and the latter are fitted by several straight-line current elements.Then,the triple integral for all the straight-line current elements is simplified into simple integral equation to which the numerical solutions are given.To solve the integral equations quickly,some integral equations are derived for the magnetostatic field,including such shapes of current elements as trapezoidal prism,triangle prism and trapezoidal sheet.Numerical results show that the calculated values conform well with the theoretical values.