The adhesional electrification force between randomly rough surfaces with identical materials

I present a general theory for the adhesional electrification and find a necessary force to separate two identical rough plates. This theory is a continuation of the previous research. In addition to the effect of the fluctuations of charge density, the roughness effects of two identical plates are considered. When both surfaces are rough but uncorrelated results an increase in the electroadhesion force in comparison to the case of only one rough surface. The roughness leads to an increase in the area of the rough surfaces as well as the magnitude of the positive and negative charges on the surfaces and this leads effectively to a larger charge induction. Therefore, the electroadhesion force increases between two rough plates by growing the magnitude of charges on the surfaces. When there is a cross correlation between two surfaces, the perturbed force is different from the case where there is no cross correlation between two surfaces for the constant charge density. As a result, if the cross correlation between two surfaces is positive (negative), the perturbed force is smaller (larger) than the case of two uncorrelated rough surfaces.