It is found experimentally that the electric field in a certain region of Earth\

Question

It is found experimentally that the electric field in a certain region of Earth's atmosphere is directed vertically down. At an altitude of 280 m the field has magnitude 60.0 N/C. At an altitude of 130 m, the magnitude is 100 N/C. Find the net amount of charge contained in a cube 150 m on edge, with horizontal faces at altitudes of 130 and 280 m. Neglect the curvature of Earth For each face, did you use an area vector that is directed outward from the cube? Did you take a dot product of that vector and the electric field vector that pierces the area? Do you realize that if the field vector skims the surface, the flux is zero?

Explanation / Answer

Net electric flux through the cube = fux through top surfcae + flux through the bootom surfcae

= -60*150^2 + 100*150^2

= 9*10^5 N.m^2/C

now using Gauss' law

net elctric flux through a closed surface = Qin/epsilon

9*10^6 = Qin/epsion

Qin = 9*10^5*8.854*10^-12

= 7.97*10^-6 C

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