Question

A square plate of copper with 53.0 cm sides has no net charge and is placed in a region of uniform electric field of 77.0 kN/C directed perpendicularly to the plate. Find the charge density of each face of the plate.
The charges will be equal and opposite for the two faces. I suggest you apply Gauss' law to a "pillbox-shape" volume with one surface above the copper and one between the two surface of the copper.
There will be no E field coming out of the lower surface, because it is a conductor.

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