Question

Question 2.35: In a Van de Graaff type generator a spherical metal shell is to be a 15 × 10 6 V electrode. The dielectric strength of the gas surrounding the electrode is 5 × 10 7 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.)

Class 12 - Physics - Electrostatic Potential And Capacitance Electrostatic Potential And Capacitance Page-92

Answer 1

$V=15\times10^6V,E=5\times10^7V/m\\\\As\:\:\:V=\frac{1}{4\pi\epsilon_0}\frac{q}{R}\:and\:E=\frac{1}{4\pi\epsilon_0}\frac{q}{R^2}\\\\V=ER\\\\R=\frac{V}{E}$

$R=\frac{15\times10^6}{5\times10^7}=3\times10^{-1}m=30cm$

hence, minimum radius of the spherical shell is 30cm