Polarizability of conducting and dielectric agglomerates:: theory and experiment

A method has been described for calculation of the dipole moment, when polarized in an electric field, of agglomerates of spherical particles of any specified size and arrangement, and of both conducting and dielectric materials. The polarization of each spherical component of an agglomerate of conducting spheres is represented by a real charge and a dipole moment in a general direction. Within the constraints of zero net charge the problem can be solved self-consistently. As a check on the validity of the method it is possible to plot contours of the constant potential surface for such an agglomerate, and these are shown to coincide closely with the geometric surface. The theoretical predictions are, for the case of linear agglomerates of limited length, verified by direct measurement of force on large scale models in spatially varying electric fields designed so that the polarization force is only weakly dependent on position. The theory is also applied to dielectric agglomerates but in this situation no net charge develops on any of the component spheres. The induced dipole moment, especially in the situation where the agglomerate is aligned parallel to the field, is much smaller than that of a conductor with the same shape. The functional relationship of the induced dipole moment per unit volume of an infinitely long linear agglomerate aligned perpendicular to the field lies between the theoretical form for an isolated sphere and that for an infinitely long cylinder. That for a sheet of spheres lies between the form for an infinite cylinder and an infinite sheet of dielectric.