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  4. The earth has volume V and surface area A, then capacitance would be

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Q. The earth has volume V and surface area A, then capacitance would be

BVP MedicalBVP Medical 2009

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} $