It has been experimentally observed that the electric field in a large region of earth's atmosphere is directed vertically down. At an altitude of 300 m, the electric field `60 Vm^(-1)`. At an altitude of 200 m, the field is 100 V m^(-1), the field is `100 Vm^(-1)`. Calculate the net amount of charge contained in the cube of 100 m edge, located between 200 and 300 m altitude.

Answer

`3.54 xx 10^(-6) C`

Explanation

`phi_E = int_(Bottom) vecE_1dvecS + int_(Top) vecE_2dvecS + 4 int_(Vertical) vecEdvecS`
`= int_(Bottom)E_1dScos0^@ + int_(Top)E_2dScos180^@ + 4int_(Vertical)EdScos90^@`
`= int_(Bottom)E_1dS - int_(Top)E_2dS = E_1S - E_2S = (E_1-E_2)S`
Also,
`phi_E = q/epsilon_0`
`q = epsilon_0(E_1-E_2)S`
`= (8.85 xx 10^(-12)C^2N^(-1)m^(-2))`
`xx (100 Vm^(-1) - 60 V m^(-1)) (100m)^2`
`= 3.54 xx 10^(-6)C`.