Abstract In eddy current testing, probe-coils with the E-type pot core are commonly used for detecting defects in test objects. In this paper, an analytical mathematical model of such a probe placed above a two-layered conductive material with a surface hole has been presented. The final formulas in the closed form that make it possible to calculate the coil impedance were worked out using the truncated region eigenfunction expansion (TREE) method and implemented in Matlab. Changes in resistance and reactance were determined for both material without a hole and for space containing no conductor. The results were compared with those obtained for the air-cored coil and the I-cored coil. The correctness of the calculations was confirmed through experimental measurements and with the finite element method (FEM) in the COMSOL Multiphysics package

中文翻译：

---

计算放置在具有表面孔的导电材料上方的 E 芯线圈的阻抗

摘要 在涡流检测中，普遍采用带有E型罐芯的探针线圈来检测被测物体的缺陷。在本文中，提出了放置在具有表面孔的两层导电材料上方的这种探针的解析数学模型。使用截断区域特征函数展开 (TREE) 方法计算出闭合形式的最终公式，可以计算线圈阻抗，并在 Matlab 中实现。电阻和电抗的变化是针对没有孔的材料和不含导体的空间确定的。将结果与空芯线圈和 I 芯线圈的结果进行比较。通过实验测量和 COMSOL Multiphysics 软件包中的有限元方法 (FEM) 确认了计算的正确性