In a Van de Graff type generator a spherical metal shell is to be a 15 × 10 6 V electrode. The dielectric strength of the gas surrounding the electrode is 5 × 10 7 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.)

Question

Philoid · Accepted Answer

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