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Electrostatic Potential and Capacitance
nbsp in a van de graaff type generator a spherica...

Question:
In a Van de Graaff type generator a spherical metal shell is to be a 15 x 10⁶ V electrode. The dielectric strength of the gas surrounding the electrode is 5 x 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:

Potential difference, V = 15 x 10⁶ V

Dielectric strength of the surrounding gas = 5 x 10⁷ V/m

Electric field intensity, E = Dielectric strength = 5 x 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.

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