Question

Taking the earth to be a spherical conductor of diameter $12.8\times 10^{3}km$ . Its capacity will be:

• A. $711\mu F$
• B. $611\mu F$
• C. $811\mu F$
• D. $511\mu F$

Answer 1

Answer: (A)

Here: Diameter of earth
$=12.8\times 10^{3}km$
Sa, radius $R=\frac{12.8}{2}\times 10^3$
$=6.4\times 10^{3}km=6.4\times 10^{6}m$
Capacity $C=4\pi {\epsilon }_{0}R$
$=\frac{1}{9\times 10^9}\times 6.4\times 10^6$
$=711\times 10^{-6}F=711\mu F$