Dielectric response of graded spherical composites

We investigate the effective dielectric responses of graded spherical composites under an external uniform electric field by taking the dielectric function of spherical inclusion, epsilon(i) = cr(k) e(beta r), where r is the inner distance of a point inside the particle from the centre of the spherical particle in the coordination. In the dilute limit, our exact result is used to test the validity of differential effective dipole approximation (DEDA) for estimating the effective response of graded spherical composites and it is shown that the DEDA is in excellent agreement with the exact result.