Magnetic polarisability of small apertures: analytical approach

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Abstract
A new method is proposed for the analysis of the magnetic polarisability of small apertures of arbitrary shape. The method is based on an integral representation for the reciprocal distance between two points previously obtained by the author. A general formula is derived for the coefficients of magnetic polarisability of small apertures. Specific formulae are obtained for the apertures shaped as a polygon, a triangle, a rectangle, a rhombus, a circular sector and a circular segment. All the formulae are checked against the solutions known in the literature and their accuracy is confirmed.

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