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A Van de Graaff generator has a spherical metal shell as an electrode which is at a potential $15 \times 10^6 \mathrm{~V}$. If the dielectric strength of the surrounding medium is $5 \times 10^7 \mathrm{Vm}^{-1}$, then the diameter of the shell is
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60 cm
Potential difference, $V=15 \times 10^6 \mathrm{~V}$
Dielectric strength of medium $=5 \times 10^7 \mathrm{~V} / \mathrm{m}$
Electric field intensity,
$$
E=5 \times 10^7 \mathrm{~V} / \mathrm{m}
$$
Minimum radius of spherical shell required for the purpose is given by
$$
r=\frac{V}{E}=\frac{15 \times 10^6}{5 \times 10^7}=0.3 \mathrm{~m}
$$
Hence diameter, $d=2 r=0.6 \mathrm{~m}=60 \mathrm{~cm}$
Dielectric strength of medium $=5 \times 10^7 \mathrm{~V} / \mathrm{m}$
Electric field intensity,
$$
E=5 \times 10^7 \mathrm{~V} / \mathrm{m}
$$
Minimum radius of spherical shell required for the purpose is given by
$$
r=\frac{V}{E}=\frac{15 \times 10^6}{5 \times 10^7}=0.3 \mathrm{~m}
$$
Hence diameter, $d=2 r=0.6 \mathrm{~m}=60 \mathrm{~cm}$
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