Class 12 Physics, CBSE and UP Board, Electrostatic Potential and Capacitance, Additional Exercise,Chapter-2 Exercise 2.35,NCERT Solutions for Class 12 Physics
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.)
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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,
r = V/E = (15 x 106 )/(5 x 107) =0.3m =30cm
Hence, the minimum radius of the spherical shell required is 30 cm.