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 $C =4\, \pi \varepsilon_{0} R$
$=\frac{1}{9 \times 10^{9}} \times 6.4 \times 10^{6}$
$=711 \times 10^{-6} F =711\, \mu F$