Volume average demagnetizing tensor of rectangular prisms

An exact analytic formula is presented for the magnetostatic field produced by a three-dimensional array of uniformly magnetized rectangular prisms. It is derived from the volume integration of a point-function demagnetizing tensor. The values of the point-function demagnetizing tensor at the centers of rectangular prisms of different aspect-ratios are compared with the volume averaged ones. This difference for the zz-component of demagnetizing tensors reaches 35% at its maximum when the aspect-ratio is 2.