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Electric field in a grounded conductor



I am having a very hard time explaining this question from "Physics" by
Eugene Hecht 1994 (p. 619 # 3)

"Figure Q3 shows a dipole in a room (which is represented by a large
grounded conductor). Make a rough sketch of its E-field and explain your
reasoning."

I would reason that the electric field inside the box would behave as if the
box weren't there. Outside the box, there shouldn't be any field. What
about at the inside and outside surface of the box?