AI 中文总结
本文利用标准实验室器材，通过四点开尔文传感方案，以相对磁导率为参数演示工频下的趋肤效应，发现铁磁性结构钢的交流阻抗显著激增，可用于本科教学。
AI 中文摘要
当交流电通过导体时，感应的内部涡流会抑制导体芯部的电流流动，将电流限制在很薄的表面层内。这种被称为趋肤效应的现象几乎在所有本科电动力学课程中都会涉及，但很少在没有专业昂贵设备的情况下通过实验探究，有时甚至被认为仅仅是高频现象。本文中，我们仅使用标准实验室器材（交直流电源、基础万用表、实验室支架作为圆柱形导体），提供了一种易于获取的工频下趋肤效应定量演示方法。基于能够分辨毫欧级电阻的精确四点开尔文传感方案，我们利用相对磁导率而非高频作为控制趋肤深度的核心参数。对于非磁性不锈钢，工频属于电动力学上的低频，其交流与直流行为完全相同；而对于铁磁性结构钢，高磁导率将趋肤深度压缩至毫米级，导致交流阻抗急剧激增。这产生了违背直觉的结果：静态性能更优的导体出现显著的相对阻抗升高，而性能较差的导体则不受影响，这挑战了学生的普遍预期并促进了认知激活。根据教学场景的不同，该方法既可以作为快速的课堂演示，也可以作为本科实验课程中的定量实验开展。
英文摘要
When alternating current flows through a conductor, induced internal eddy currents suppress current flow in the core and restrict it to a thin surface layer. Although this effect, known as the skin effect, is covered in virtually every undergraduate electrodynamics course, it is rarely explored experimentally without specialized and expensive equipment, and is sometimes even considered a mere high-frequency phenomenon. Here, we present a readily accessible, quantitative demonstration of the skin effect at line frequency using only standard laboratory supplies: an AC/DC power supply, basic multimeters, and laboratory support rods as cylindrical conductors. Based on a precise four-point Kelvin sensing scheme capable of resolving milliohm-range resistances, we exploit relative magnetic permeability rather than high frequency as the governing parameter to control skin depth. For non-magnetic stainless steel, line frequency represents an electrodynamically low frequency, resulting in identical AC and DC behaviour; whereas for ferromagnetic structural steel, high permeability compresses the skin depth to the millimeter scale, causing a sharp surge in AC impedance. This produces a counterintuitive outcome where the statically superior conductor suffers a marked relative impedance increase, whereas the poorer conductor remains unaffected, challenging common student expectations and catalyzing cognitive activation. Depending on the instructional setting, the approach can be implemented either as a quick lecture demonstration or as a quantitative experiment within an undergraduate laboratory course.
