Surface Coulomb problem dipole moments

When solving problems involving the calculation of forces of electrostatic interaction between two conducting particles, approximations of dipole, dipole-coulomb, and coulomb interactions are frequently used. Within the framework of these approximations, particle interactions are considered as interactions of two electric dipoles, a dipole and a point charge, or two point charges. Here, the sizes of the particles define only the values of the dipole moments. Therefore, such approximations may only be used if the distance between the particles is much greater than the sum of their radii. However, in practice, these approximations are frequently used when the gap between the surfaces of the particles is comparable to or less than the size of the particles. Consequently, this raises doubts concerning the accuracy of cited approximations for various distances between particles. 

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