Recently, the magnetic field penetration through a circular aperture in a thin perfect electric conductor when excited by a loop antenna placed coaxially with the aperture is solved analytically in the quasi-static frame. However, the analytical solution is only applicable to the longitudinal component. Here, we present two approaches to obtain the transverse component. The first one belongs to the direct extension of the earlier results, but lengthy mathematic derivations are performed to solve a complex integral. The second one utilizes the magnetic vector potential formulation and then converts it into a known scalar potential problem.

中文翻译：

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关于“通过完美导电板上的圆孔的低频磁场穿透的分析模型”的笔记

最近，当由与孔径同轴放置的环形天线激励时，通过薄完美电导体中的圆形孔径的磁场穿透在准静态框架中被解析解决。然而，解析解仅适用于纵向分量。在这里，我们提出了两种获得横向分量的方法。第一个属于早期结果的直接扩展，但需要进行冗长的数学推导来求解复杂的积分。第二个利用磁矢量势公式，然后将其转换为已知的标量势问题。