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

Point electrodes at high voltage are used in many diverse electrostatic particle charging and deposition applications, such as electrostatic liquid and powder coating, aerosol and ash filtrations, and pesticide spraying of agricultural crops. The electric field and the space charge generated by the high voltage electrode are important parameters for particle charging and particle deposition. To improve system design and application, these two parameters must be calculated as accurately as possible in the charging zone at the electrode tip, in the deposition zone at the target surface and in the transport zone in-between. The independent parameters are the electrode voltage and its shape and the target distance and its shape. An ideal spherically symmetric case is presented where the high voltage electrode is a sphere of radius r₀ at voltage V₀, concentric with a grounded conductive sphere of radius R₀. This ideal case is the closest to represent a point electrode facing grounded targets at certain distance away for which an analytical solution of Poisson´s equation can be obtained. It produces electric field formulas applicable to real situations. Unlike the existing numerical methods, this analytical solution explains the relationships between various parameters which are necessary for design and optimization. Also, the experimental results suggest a minimum value for ion mobility which is more in line with the value suggested by A.D. Moore for dry air of 2.1×10^-4 m²/v.s