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(C) The potential of the spherical shell is given as $V = 15 	imes 10^6 \,V$.The dielectric strength of the surrounding medium, which represents the

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$60$

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(C) The potential of the spherical shell is given as $V = 15 	imes 10^6 \,V$.The dielectric strength of the surrounding medium, which represents the maximum electric field intensity $E$ the medium can withstand before breakdown, is $E = 5 	imes 10^7 \,V/m$.For a spherical shell of radius $r$, the potential is related to the electric field at its surface by $V = E 	imes r$.Therefore, the minimum radius $r$ required is $r = \frac{V}{E}$.Substituting the given values: $r = \frac{15 	imes 10^6 \,V}{5 	imes 10^7 \,V/m} = 0.3 \,m$.The diameter $d$ of the shell is $d = 2r = 2 	imes 0.3 \,m = 0.6 \,m$.Converting to centimeters, $d = 0.6 	imes 100 \,cm = 60 \,cm$.

$A$ Van de Graaff generator has a spherical metal shell as an electrode which is at a potential $15 \times 10^6 \,V$. If the dielectric strength of the surrounding medium is $5 \times 10^7 \,V/m$, then the diameter of the shell is (in $\,cm$)

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