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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 $6.4 \times 10^6 \mathrm{~m}$.
Options:
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 $6.4 \times 10^6 \mathrm{~m}$.
Solution:
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Verified Answer
The correct answer is:
Statement 1 is true, Statement 2 is false.
Statement 1 is true, Statement 2 is false.
Capacitance of sphere is given by:
$C=4 \pi \epsilon_0 r$
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 $711 \mu \mathrm{F}$.
$C=4 \pi \epsilon_0 r$
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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