In a Van de Graaff type generator a spherical metal shell is to b… - Vidyadip

Question

In a Van de Graaff type generator a spherical metal shell is to be a 15 × 10⁶V electrode. The dielectric strength of the gas surrounding the electrode is 5 × 10⁷Vm^–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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Answer

Potential difference, V = 15 × 10⁶V
otelectrtc strength of the surrounding gas $={5}\times{10}^{7}\frac{\text{V}}{\text{m}}$
Electric field intensity, E = Dielectric strength $= {5}\times {10}^{7}\frac{\text{V}}{\text{m}}$
Minimum radius of the spherical shell required for the purpose is given by,
$\text{r}=\frac{\text{V}}{\text{E}}$
$=\frac{15\times10^{6}}{5\times{10}^{7}}={0.3}\text{m}={30}\text{cm}$
Hence, the minimum radius of the spherical shell required is 30cm.

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