A hypothesis on electrical field distribution is presented for the physical model of a scanning probe tip with a conical body ending in a spherical apex. Based on the hypothesis, we deduced an analytical model to calculate the electrostatic force acting on the tip and analyzed variation of the electrostatic force with structural parameters of the tip. The simulation results are consistent with those given by numerical methods of equivalent charge distribution (ECD) and by experiments. The hypothesis is proved reasonable according to the work.

Based on Hamaker's hypothesizes and Lennard-Jones potential, a model of rigid sphere-panel nano-contact was presented to solve microcollision and nanocontact problems. The adhesion equations between the sphere and the first layer atoms or the N layer atoms of the panel were obtained by a continuum method. It is shown that the Hamaker's micro continuum medium principle is held only as the interaction distance 7 times greater than the atomic radius.

Based on three Hamaker hypothesizes and Lennard-Jones potential, the model of rigid sphere-panel nano-contact is presented to solve the micromechanic "microcollision" and "nanocontact" problems, and the adhesion equations between the sphere and the first layer atom or the N layer atom of the panel are obtained by continuum method. The conclusion shows that the principal atoms affecting nanocotact force are the minority layers closing the contact zone.