Uniform field charge on a conducting particle

The charge on a conducting particle in an infinite uniform field or standing on a ground plane in a uniform background field is important to a range of technical areas, such as particle motion in gas-insulated substations. This charge is normally evaluated based on an approximate formula which is often traced back to an obscure paper over 40 years ago. Software technology now facilitates the solution of many such problems exactly, which allows evaluation of (i) the approximation and (ii) the range of parameters over which the approximation is accurate.