Question

On a clear day, the Earth’s atmospheric electric field near the ground has a magnitude of 100 N/C and points vertically down. Inside the ground, the electric field is zero, since the ground is a conductor. Consider a mathematical box of 1.0 m x 1.0 m x 1.0 m, half below the ground and half above. What is the electric flux through the sides of the box? What is the charge enclosed by the box?

Answer 1

Use Gauss' Law. Assume there is no flux in the downward direction or out the sides. The flux through the top (E* 1 m^2) will be proportional to the charge inside the box. Look up the law for the poprtionality constant.

That charge will reside at the surface, since the groud is a conductor.