Theoretical field configurations for thundercloud models with volume charge distributions

The potential gradient at ground level due to a charge volume is obtained in terms of integrals, some values of which are computed as functions of normalized vertical and horizontal distances. Using these values the vertical potential gradients at points on the ground below some simple cloud volumes, built up of cylindrical slices of uniform charge densities, are calculated. The results consitute definite improvements on those provided by conventional point-charge models.