Question

In a Van de Graaff type generator a spherical metal shell is to be a15 × 106 V electrode. The dielectric strength of the gas surroundingthe electrode is 5 × 107 Vm–1. What is the minimum radius of thespherical shell required? (You will learn from this exercise why onecannot build an electrostatic generator using a very small shellwhich requires a small charge to acquire a high potential.)

Answer 1

Given: The potential difference is 15× 10 6  V and the dielectric strength of the surrounding gas is 5× 10 7  V/m

The electric field intensity is the dielectric strength of the gas.

The required minimum radius of the spherical shell is given as,

r= V E

Where, the potential difference is V and the electric field intensity is E.

By substituting the given values in the above equation, we get

r= 15× 10 6 5× 10 7 =0.3 m =30 cm

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