Question

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 $6.4\times 10^{6}m$.

• A. Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.
• B. Statement 1 is false, Statement 2 is true.
• C. Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.
• D. Statement 1 is true, Statement 2 is false.

Answer 1

Answer: (D)

Capacitance of sphere is given by :
$C=4\pi {\in }_{0}r$
If, $C=1F$ then radius of sphere needed :
$r=\frac{C}{4\pi {\in }_0}=\frac{1}{4\pi \times 8.85\times 10^{-12}}$
or, $r=\frac{10^{12}}{4\pi \times 8.85}=9\times 10^{9}m$
$9\times 10^9$ m is very large, it is not possible to obtain such a large sphere. Infact earth has radius $6.4\times 10^6$ m only and capacitance of earth is $711\mu F.$