Electric field and space charge of spherical electrode at high voltage concentric with a grounded conductive sphere

The solution of the space-charge Poisson´s equation is presented for a spherical electrode at high voltage concentric with a grounded conductive sphere. The obtained electric field is given in terms of the ion current emitted by the electrode and an integration constant. Both parameters are functions of boundary conditions. Using measured values of the ion current for a range of boundary conditions and applying these boundary conditions to determine the integration constant suggest a minimum value for the ion mobility of 1.9×10^-4 m² /V.s. Approximate formulas for the ion current and the electric field in terms of the independent parameters were also developed. Also, it was shown that this spherical system with its solution can be used to make accurate evaluation of the ion mobility. The obtained solutions can be applied with good approximation to many practical electrostatic systems involving point electrode at high voltage generating ions. Although the subject matter is very general and could have a fundamental research aspect, in this paper, it is meant to be applied to the area of electrostatic powder paint coating. Therefore, all the examples of boundary conditions and illustrations are typical of the electrostatic powder paint coating