Stability analysis of a spherical electrostatic suspension in a liquid in the induction approximation

In [1] the image force was shown to impose additional conditions for the electrostatic suspension of a sphere without dynamic control of the electrode potential, and the dependence of the critical voltage between the electrodes on the sphere radius was derived experimentally. In this work, this dependence is found analytically by calculating electrical forces in the third-order approximation in shift of the sphere from equilibrium.