This letter proposes an approximate analytical formulation for the shielding problem of a perfectly electric conducting disk against the low-frequency magnetic field produced by a circular current loop placed coaxially with the disk. First, this problem is related to a complementarity problem: The leakage of the magnetic field through a circular hole on a perfectly magnetic conducting plane of infinite extension. Then, for the complementarity problem, we develop the accurate analytical solution if only the distribution of the normal component of the unshielded magnetic field along the surface of the hole can be expressed as a polynomial function of radial distance. The analytical formulation is verified with finite element simulations and measured results.

中文翻译：

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完美导电圆盘的低频磁屏蔽：考虑发射环半径的近似解析公式


这封信提出了一个近似解析公式，用于解决完美导电盘对与盘同轴放置的圆形电流环产生的低频磁场的屏蔽问题。首先，这个问题与互补问题有关：磁场通过无限延伸的完美导磁平面上的圆孔泄漏。然后，对于互补问题，只要非屏蔽磁场的法向分量沿孔表面的分布可以表示为径向距离的多项式函数，我们就可以得到精确的解析解。通过有限元模拟和测量结果验证了解析公式。