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The electric field in a large region of earth’s atmosphere is directed vertically down. At an altitude of 300m, the electric field is 60 V/m. At an altitude of 200 m, the electric field is 100 V/m. The net amount of charge contained in the cube of 100m edge, located between 200m and 300m altitude is:

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3.54 $μC$

5.43 $μC$

300 $μC$

100 $μC$

answer is A.

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Detailed Solution

Flux entering at 300 m = $60 \times (100)^{2}$
Flux leaving at 200 m = $100 \times (100)^{2}$
Net flux,

$ϕ_{2} - ϕ_{1} = 40 \times 10^{4} = \frac{q}{ϵ_{0}}$
$\begin{array}{rcl} q & = & 4 \times 10^{5} \times 8 .85 \times 10^{- 12} \\ = & 35 .4 \times 10^{- 7} \\ = & 3.54 μC \end{array}$

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