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(B) The capacitance of a spherical capacitor is given by $C = 4\pi \varepsilon_0 \frac{ab}{b - a}$.Here,$a$ is the radius of the Earth $= 6400 \ km =

Vedclass · Accepted Answer

$0.09$

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(B) The capacitance of a spherical capacitor is given by $C = 4\pi \varepsilon_0 \frac{ab}{b - a}$.Here,$a$ is the radius of the Earth $= 6400 \ km = 6.4 	imes 10^6 \ m$.The outer radius $b$ is the distance to the stratosphere $= 6400 \ km + 50 \ km = 6450 \ km = 6.45 	imes 10^6 \ m$.Given $\frac{1}{4\pi \varepsilon_0} = 9 	imes 10^9 \ N \cdot m^2/C^2$.Substituting the values:$C = \frac{1}{9 	imes 10^9} 	imes \frac{(6.4 	imes 10^6) 	imes (6.45 	imes 10^6)}{6.45 	imes 10^6 - 6.4 	imes 10^6}$$C = \frac{1}{9 	imes 10^9} 	imes \frac{41.28 	imes 10^{12}}{0.05 	imes 10^6}$$C = \frac{41.28 	imes 10^{12}}{9 	imes 10^9 	imes 0.05 	imes 10^6} = \frac{41.28 	imes 10^{12}}{0.45 	imes 10^{15}} \approx 0.0917 \ F \approx 0.09 \ F$.

The stratosphere acts as a conducting layer for the Earth. If the stratosphere extends up to $50 \ km$ from the Earth's surface,calculate the capacitance of the spherical capacitor formed between the Earth's surface and the stratosphere in $F$. Take the radius of the Earth as $6400 \ km$.

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