A) \[4\pi {{\varepsilon }_{0}}\frac{A}{V}\]
B) \[4\pi {{\varepsilon }_{0}}\frac{V}{A}\]
C) \[12\pi {{\varepsilon }_{0}}\frac{V}{A}\]
D) \[12\pi {{\varepsilon }_{0}}\frac{A}{V}\]
Correct Answer: C
Solution :
Volume of sphere (earth) \[=\frac{4}{3}\pi {{R}^{3}}\] Where R is the radius of the sphere. Area of the sphere \[=4\pi {{R}^{2}}\] Now, \[\frac{V}{A}=\frac{R}{3}\] ?(i) Capacitance of a sphere \[C=4\pi {{\varepsilon }_{0}}R\] ...(ii) From Eqs. (i) and (ii), we get \[C=4\pi {{\varepsilon }_{0}}\left( \frac{3V}{A} \right)=\frac{12\pi {{\varepsilon }_{0}}V}{A}\]
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