Van Der Waals Attraction Between Macroscopic Bodies

A general dispersion formula is derived, which represents the dispersion energy between two bodies A and B by their macroscopic screened fluctuation fields. These fluctuation fields are calculated exactly in the case of half-spaces and spheres. In the case of half-spaces the Lifshitz dispersion formula is obtained. The dispersion energy between spheres is found to vary as 1/d for separations d small compared with the radii and to be proportional to 1/d ⁶ for separations d large compared with the radii. The effect of layers adsorbed on the surfaces of the spheres on the dispersion energy is calculated. The dielectric properties of the adsorbed layers predominate over those of the bulk material for separations d smaller than the layer thickness.