The validity range of the dipole approximation for a dielectric mixture ☆

This paper investigates the validity range of the dipole approximation for a dielectric mixture with spherical inclusions through electric field analyses according to a new criterion: if the maximum perturbation on an arbitrarily selected sphere surface caused by the interactions among spheres is less than a given allowable error, the dipole approximation is considered acceptable. Based on the dipole-enhanced dipole approximation previously presented by us, a theoretical formula for calculating the validity range of the dipole approximation is derived. It shows that the validity range depends on three parameters, the dielectric mismatch, the volume fraction of inclusions, and the allowable error. The calculated results by this formula are compared with those numerically obtained by the FEM. The good agreement between them indicates the credibleness of this formula.