We have extended Rayleigh identity based on a multipole expansion theory to
deal with the conductivity effects in electric-field-induced electrorheolo
gical solid within a Maxwell-Wagner approach. Evaluation of the effective d
ielectric constant is emphasized and shear modulus for chains of particles
arrayed on a body-centred tetragonal (BCT) lattice is calculated, It is fou
nd that for high frequency applied electric fields, the forces and then the
modulus depend upon the dielectric constants of the suspending fluid and t
he dispersed particles, for low-frequency or de electric fields, the conduc
tivities of the components are dominant. Implications for the design of ER
fluids are discussed briefly. (C) 2000 Elsevier Science B.V. All rights res
erved.