In a Van de Graff 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.)


Potential Difference of the spherical metal shell (V) = 15 × 106 V

Dielectric strength of the gas surrounding the electrode = 5 × 107Vm-1


Dielectric strength = Electric field intensity (E)


The minimum radius of the spherical shell (r),



∴ r = 15 × 106 V/5 × 107 Vm-1 = 0.3m


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