The stratosphere acts as a conducting layer for the earth. If the stratosphere exends beyond `50 km` from the surface of earth, then calculate the capacitance of the spherical capacitor formed between strasphere and earth's surface. Take radius of earth of as `6400 km`.

Answer

`0.092 F`

Explanation

Capacity or a spherical capacitor is
`C = 4pi in_(0) (r_(a) r_(b))/(r_(b) - r_(a))`, where
`r_(a)` = radius of earth `= 6400 km = 6.4xx10^(6) m`
`r_(b)` = radius of outer layer of stratosphere
`= (6400 + 50) km = 6.45xx10^(6) m`
`:. C = (1)/(9xx10^(9)) (6.45xx10^(6) xx 6.4xx10^(6))/((6.45xx10^(6) - 6.4xx10^(6))`
`= (6.45xx6.4xx10^(1//2))/(9xx10^(9)(0.05xx10^(6))) = 0.92 F`