Taking earth to be a metallic sphere, its capacity will approximately be

Taking earth to be a metallic sphere, its capacity will approximately be
  1. \(6.4 \times 10^6 \mathrm{~F}\)
  2. \(700 \mathrm{~F}\)
  3. \(700 \mu \mathrm{F}\)
  4. \(700 \mathrm{pF}\)

Solution

Radius of earth, \(R=6400 \mathrm{~km}=6.4 \times 10^6 \mathrm{~m}\) Taking earth to be a metallic sphere, its capacitance is given as \(\begin{aligned} C & =4 \pi \varepsilon_0 R=\frac{1}{9 \times 10^9} \times 6.4 \times 10^6 \\ & =0.7111 \times 10^{-3} \mathrm{~F}=711.1 \times 10^{-6} \mathrm{~F} \\ & =711 \mu \mathrm{F}=700 \mu \mathrm{F} \end{aligned}\)

Asked in: AP EAMCET 2020 (21 Sep Shift 2)

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