Dielectric breakdown sizes of conducting plates

In this work, we propose mathematical formulations that detail the effect of the dielectric strength of dielectric material on the spatial distribution of electric field in an infinite space with a conducting plate. Using the dielectric strength of air as the maximum limit for the magnitude of electric field intensity and the equivalence of stored charge between two different zones, we determine the size of the dielectric breakdown region (the extended region with ionized material) for the conducting strip and the conducting disk charged to an electric voltage. The size of dielectric breakdown is proportional to the square of the applied voltage, and decreases with the increase of the width/radius of the conducting strip/disk.