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Consider a mathematical surface having the shape of a cube of edge 5cm.You do not know the electric charge or the electric field inside the cube , but you know the electric field at the surface; at the top of the cube the electric field has a magnitude of  5*105 N/C and points perpendicularly out of the cube; at the bottom of the cube, the electric field has a magnitude of 2*105 N/C and points perpendicularly into the cube; on all other faces, the electric field is tangential to the surface of the cube:

a) How much electric charge is inside the cube?

b) Can you guess what charge distribution inside (and outside) the cube would generate this kind of electric field?

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