Spatial shape demagnetising factors of disc, equilateral triangle and irregular hexagonal magnetic insulators

The connection between the external and internal direct magnetic field intensities in an ellipsoidal magnetic insulator in a uniform field is a classic result in the literature. It is usually stated in terms of shape demagnetising factors. The case of the non-ellipsoidal geometry in a uniform field has been dealt with in a number of approximate ways but has by and large been restricted to disc geometries in infinite space. The aim of the paper is to verify some existing relationships on the spatial dependent shape demagnetising factors of the classic disc insulator by having recourse to a static magnetic solver. The demagnetising factors along the two main coordinates of equilateral and irregular hexagonal magnetic insulators are also evaluated.