Ncert Exercises & Solutions

In a Van de Graaff type generator, a spherical metal shell is to be a \(15\times10^6~\text V\) electrode. The dielectric strength of the gas surrounding the electrode is \(5\times 10^7~\text{Vm}^{-1}.\) What is the minimum radius of the spherical shell required to avoid electrical breakdown of the gas?
1. \(0.1~\text m\)
2. \(0.3~\text m\)
3. \(0.5~\text m\)
4. \(3.0~\text m\)

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 = \frac{V}{E} = \frac{15 \times 10^{6}}{5 \times 10^{7}} = 0 .3 m = 30 cm

Hence, the minimum radius of the spherical shell required is 30 cm.

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