NEAREST-NEIGHBOR APPROXIMATION FOR THE DIPOLE-MOMENT OF CONDUCTING-PARTICLE CHAINS

The image charges due to nearest neighbors in an N-particle chain of c onducting spherical particles in a uniform electric field are solved e xactly. The contribution of these charges to the dipole moment of the chain is evaluated exactly. The dipole moment is approximately given b y p(NN) = 4/3 piepsilon0E0R3[(2ln(2) - 1)N3 + (6 - 6ln(2))N2 + (4ln(2) - 8)N + 12(N - 1) zeta(3)], where zeta is the Riemann zeta function. The results predicted by the approximate formula are compared to the n umerical calculations of Jones, including all image terms, for the cas es N = 2-4, and to our numerical calculations for N = 5-7. The approxi mation agrees with the numerical calculations to within approximately 10%, with the worst error occurring at N = 3. Comparison to the dipole moment of a cylinder is also made.