This question has Statement $1$ and Statement $2$. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement $1$ : It is not possible to make a sphere of capacity $1$ farad using a conducting material.
Statement $2$ : It is possible for earth as its radius is $6.4\times10^6\, m$
AIEEE 2012, Diffcult
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Capacitance of sphere is given by:
$C=4 \pi \in_{0} r$
If, $C=1\, \mathrm{F}$ then radius of sphere needed:
$r=\frac{C}{4 \pi \epsilon_{0}}=\frac{1}{4 \pi \times 8.85 \times 10^{-12}}$
or, $r=\frac{10^{12}}{4 \pi \times 8.85}=9 \times 10^{9}\, \mathrm{m}$
$9 \times 10^{9}\, \mathrm{m}$ is very large, it is not possible to obtain such a large sphere. Infact earth has radius $6.4 \times 10^{6}\, \mathrm{m}$ only and capacitance of earth is $711\, \mu \mathrm{F}$
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