任意同轴圆线圈互感系数的近似解析公式

为使任意大小、任意距离的两同轴圆线圈之间的互感系数能用关系简单明了的常用解析函数表示,先对用毕奥-萨伐尔定律导出的互感系数积分公式进行数值计算,然后通过对极端情况的分析和对非极端情况进行猜想,采用幂级数、指数、对数或其组合进行试探,再用数值计算验证,最终尝试性地分6种情形给出了两同轴圆线圈在任意大小、任意距离下（除两线圈几乎重合外）互感系数的近似解析表达式。函数表达式比较简单,物理意义比较明确,且相对误差在±5%以内。

The Approximate Analytic Formula of the Mutual Inductance between Two Discretionary Coaxial Loops

The approximate analytic formula of the mutual inductance between two discretionary coaxial loops（it is an exception that the loops is almost superposition）is obtained for the first time through analysis,guess and numeral calculation,and the relative error is less than ±5%.The methods are：at first,numeral calculating by using the integration formula which is proved by Biot-Shavell＇s law,secondly,analyzing the extremeness,and guessing the common status by using power function,exponential function,logarithmic function and their compounding,finally,validating by numeral calculation.