A methodology is described in this paper for computing the quasi-static eff
ective permittivity of a two-dimensional (2-D) or three-dimensional (3-D) l
attice of dielectric particles. The particles in this composite material ma
y have complicated shapes. This methodology uses a moment method based tech
nique to determine the electric dipole moments of the particles immersed in
a uniform electric field. The effective permittivity is then obtained usin
g an appropriate macroscopic model. With this methodology, the mutual inter
action between particles can be accounted for accurately. The computed effe
ctive permittivity for round cylinders and spheres suspended in a host are
compared with our previous T-matrix method results as well as the Maxwell G
arnett (MG) formula predictions. Three additional examples involving square
(2-D), rounded square (2-D), and spherical (3-D) dielectric inclusions are
also given, illustrating the shape effects on the computation of the quasi
-static effective permittivity. While the square- and cubic-shaped particle
s can possess great mutual interaction, surprisingly their effective permit
tivity is well predicted for all volume fractions by the simple MG formula
in both 2-D and 3-D problems.