Electric forces among nanospheres in a dielectric host

The force among a collection of dielectric spheres, suspended in a different dielectric host and subject to a uniform instantaneous external electric field, has been calculated as a function of the various parameters of the problem. A new approach is used to do this which is essentially exact: No assumptions are made regarding the smallness of spatial separation of neighboring spheres or the closeness of the two permittivities. In particular, the spheres can be metallic and the separation can be much smaller than the two radii. As an example, the case of two spheres is discussed in detail. Also discussed is the force acting on the smallest sphere in a nano-lens configuration of three linearly aligned metallic spheres whose sizes and separations diminish consecutively in a self-similar fashion. Actually, the approach can be applied to find the force acting on any sphere in larger collections of spheres, subject to an external field which points in an arbitrary direction. Possible applications include simulations of electrorheological fluids.