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(D) The electric field $E$ at the surface of a conducting sphere of radius $r$ is given by $E = \frac{V}{r}$,where $V$ is the potential of the sphere.

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$10^6\,V$

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(D) The electric field $E$ at the surface of a conducting sphere of radius $r$ is given by $E = \frac{V}{r}$,where $V$ is the potential of the sphere.Given,the maximum electric field $E_{max} = 10^7\,V/m$ and the radius $r = 0.10\,m$.To find the maximum potential $V_{max}$,we use the relation $V_{max} = E_{max} 	imes r$.Substituting the values: $V_{max} = 10^7\,V/m 	imes 0.10\,m$.$V_{max} = 10^7 	imes 10^{-1} = 10^6\,V$.Thus,the maximum potential to which the sphere can be charged is $10^6\,V$.

The maximum electric field that can be held in air without producing ionization of air is $10^7\,V/m$. The maximum potential,therefore,to which a conducting sphere of radius $0.10\,m$ can be charged in air is:

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