In a Van de Graaff type generator a spherical metal shell is to be a 15 × 106 V electrode. The dielectric strength of the gas surrounding the electrode is 5 × 107 Vm−1. What is the minimum radius of the spherical shell required? (You will learn from this exercise why one cannot build an electrostatic generator using a very small shell which requires a small charge to acquire a high potential.)
Potential difference, V = 15 × 106 V
Dielectric strength of the surrounding gas = 5 × 107 V/m
Electric field intensity, E = Dielectric strength = 5 × 107 V/m
Minimum radius of the spherical shell required for the purpose is given by,
Hence, the minimum radius of the spherical shell required is 30 cm.