In order to calculate the average growth of a charged particle in a dust cloud caused by electrostatic attraction, the following assumptions were made: the particles obey Stokes' law of motion, their velocities are small so that their motion can be considered to be in constant equilibrium with the forces acting, and the forces are effective at short ranges only or the cloud density is small enough so that not more than two particles have to be considered interacting at a time. In addition to the Coulomb force, there will appear an attraction between particles resulting from induced dipoles, but it was found that in general the effect of this force can be neglected. Straight forward integration of the equation of relative motion of two charged dust particles yields their effective cross section for aggregation from which in turn we can determine the rate of growth if the particle size and charge distribution in the cloud is known. Assuming a highly simplified distribution, one arrives at the result that aggregation is negligible if the cloud density is less than a million particles per cm3 or if the average charge of one sign is well below a thousand electrons per particle.