Question

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.)

Answer 1

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,

`r=V/E`

`=(15xx10^6)/(5xx10^7)=0.3m=30cm`

Hence, the minimum radius of the spherical shell required is 30 cm.