Electric field, potential and capacitance of a sphere-plane electrode system

The electrostatic field, potential and capacitance of a sphere-plane electrode system are investigated theoretically. Previous work has been confined to the evaluation of the fields at points on the surface of the sphere and along the axis of symmetry. In this work, the electrostatic field at any point in the system is considered. The knowledge of the behaviour of the field at points away from the axis is important in connection with the study of electron avalanches in such a gap. A Table showing the convergence of the series equations for the field and potential distribution in the gap for several gap/radius ratios is given, and the expression for the capacitance of the system is compared with approximate expressions derived previously.