Abstract: The analytical expressions of effective dipole moment and quadrupole moment for a dielectric sphere with an eccentric spherical inclusion under the influence of a static uniform external field are obtained by using the variable separation. The approximate effective permittivity （AEP） of dielectric sphere with an eccentric spherical inclusion is introduced. Because the AEP is related not only to the dielectric inside the sphere but also to the dielectric outside the sphere, it is unlike the equivalent permittivity of concentric layered dielectric sphere. The variation of AEP with the eccentricity and permittivity of dielectric outside the sphere is shown by numerical results.

Key words: eccentric spherical inclusion, eccentricity, effective permittivity