On the Shape of a Charged Drop in the Electrostatic Field of an Extended Spheroid Supported at a Constant Electric Potential

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In asymptotic calculations, the equilibrium shape of a charged drop is found in a non-uniform electrostatic field created by an extended spheroid modeling a rod supported at a constant electric potential. It has been found that the size of the small axis of the spheroid (thickness of the rod) that creates the field markedly affects the equilibrium shape of the charged drop. The distortion of the spherical shape of the surface of the charged conducting drop of an ideal incompressible liquid in a non-uniform electrostatic field of the rod can be approximately described by the superposition of the excited second and third modes, the amount of which is determined by the required degree of precision of the description.