磁偶极子源电磁场代数解与积分解的数值计算

Numerical calculation of magnetic dipole electromagnetic field with its algebraic form and integral expression

近年来计算物理在大学物理教育中愈加受到关注.本文由麦克斯韦方程出发,通过引入赫兹势,推导出磁偶极子源在均匀介质中激发的电磁场的代数表达式及其相应的积分表达式.采用三次样条拟合与高斯-勒让德数值积分方法联合求解其积分解,并与其代数解进行数值验证,为学生提供一个既有物理背景又有数值计算方法的电动力学计算案例.

In recent years,computational physics has attracted more and more attention in college physics education.In this paper,we derive the algebraic form and the integral expression of electromagnetic field excited by magnetic dipole source in uniform medium.The solution is solved by introducing Hertz potential based on Maxwell equations.Cubic spline fitting method and Gauss-Legendre numerical integration method are used to solve this numerical integral problem,and its numerical results are verified with the algebraic form.It also provides students an electrodynamics calculation case including both physical background and numerical calculation method.