It has been experimentally observed that the electric field in a large region of earths atinosphere is directed vertically down. At an altitude of 300 m, the electric field is 60 vm-1 . At an altitude of 200 m, the field is 100 vm-1. Find the net amount of charge contained in the cube of 100 m edge, located between 200 m and 300 m altitude is

According to Gauss' theorem, electric flux: ϕE=qε0=∫E→·dS→The surface integral in the above equations contains six terms - the surface integral over the bottom surface, the surface integral over the top surface and surface integral over the four vertical faces . For the bottom surface, both the vectors E→ and dS→ are in the same direction. For the top surface, they act in opposite directions while for the vertical aces, they are perpendicular to each other. Hence, ϕE=∫bottom E→1·dS→+∫top E→2·dS→+4∫faces E→.dS→ =∫bottom E1·dScos0°+∫top E2·dScos180°+4∫faces EdScos90° =∫bottom E1·dS-∫top E2·dS=E1S-E2S=E1-E2S Also, ϕE=qenclosed ε0q=ε0E1-E2S=ε0100Vm-1-60Vm-1(100 m)2 =4×105ε0C