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In a Van de graaf type generator a spherical metal shell is to be a 15xx10^(6) volt electrode. The dielectric strength of the gas surrounding the electrode is 5xx10^(7) Vm^(-1). What is the minimum radius of the spherical shell required ? <br> [you will learn form this exercise why one cannot build an electrostatic generator using a very small shell, which requires a small charge to acquire a high potential.]

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Answer Text

Solution :
potential difference , `V=15xx10^(6) V` <br> Dielectric strength of the surrounding gas `=5xx10^(7) V//m` <br> Electric field intensity, E=dielectric strength =`5xx10^(7)V//m` <br> Minimum radius of the spherical shell require for the purpose is given by <br> `r=V/E` <br> `=(15xx10^(6))/(5xx10^(7))=0.3 m =30 cm `<br> Hence, the minimum radius of the spherical required is 30 cm .

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