A displaced dipole model for spheres in a non-uniform field

In this paper, a displaced dipole model for spheres in a non-uniform field is proposed. The displaced dipole moment and displacement can be approximately obtained from the external field values at the two poles of the sphere. The analytical expressions of the electric field are derived for a sphere in the non-uniform electric field. As the model does not have to assume the external field to be uniform in the vicinity of the spheres, it differs from the dipole-at-the-center approximation. In addition, it is simpler than the multipoles technique. Another result obtained is that the displaced dipole of two closely spaced spheres approaches the edge of the sphere when εi/εe⩾4 and the displaced dipole model becomes ineffective.