Calculation of field factor for a vertical sphere gap, taking account of surrounding earthed surfaces

Using a digital computer, field factor has been calculated for spherical electrodes by the image-charge method, taking account of adjacent plane or spherical boundary surfaces. The method has been applied to a vertical asymmetric sphere gap represented by a pair of spheres above an infinite earth plane or a pair of spheres within an enclosing earthed sphere. Graphs are presented showing the percentage increase in field factor above the value applicable to isolated spheres, for different positions of the boundary surface; these graphs enable values of field factor to be deduced, for the geometries represented, with an accuracy better than 0.1%. For the standard sphere gap of BS3581 and IEC52,2 varying the position of the infinite earth plane over the full permitted range leads to changes of up to 0.4% (±0.2%) in field factor, for a gap spacing of one sphere radius. When the clearance from the sphere gap to additional earthed surfaces, representing the walls and ceilings of a laboratory, is varied from the minimum value permitted to about five times this value, with the earth plane as close to the sphere gap as allowed, the field factor falls by 0.5%.