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导电导磁球和轴对称线圈的共轴电磁系统可用于球的涡流无损检测。文章利用磁矢量位和洛仑兹规范，建立了均匀导电导磁球和圆环线圈共轴电磁系统的时谐场边值问题，用分离变量法求解得到了球的散射场解析解。在此基础上，导出了球和空芯圆柱线圈共轴电磁系统的电磁场解析解和线圈的阻抗增量解析式。为便于计算，给出了复宗量的球贝塞尔函数的计算方法。实验表明，阻抗增量的理论计算值和实验测量值符合程度良好。文中的分析过程表明，所得解析方法同时也适用于分层球和任意截面的轴对称线圈的共轴电磁系统。
Coaxial electromagnetic systems with conductively-conducting balls and axially symmetric coils can be used for ballistic eddy current non-destructive testing. In this paper, by using the magnetic vector and Lorentz standard, the boundary value problem of the harmonic field of a coherent electromagnetic conducting system with uniformly conducting and conducting coils and a toroidal coil is established. The analytic solution of the scattering field of a sphere is obtained by the method of separating variables. On this basis, the analytic solution of the electromagnetic field of the coaxial electromagnetic system of the ball and the hollow cylindrical coil and the analytical solution of the impedance increment of the coil are deduced. In order to facilitate the calculation, the calculation method of the Bessel function of the complex number is given. Experiments show that the theoretical value of the impedance increase is in good agreement with the experimental value. The analytical process in this paper shows that the analytic method is also applicable to the coaxial electromagnetic system of axisymmetric coils with layered spheres and arbitrary cross sections.