Posted by Melissa on Friday, February 3, 2012 at 11:57pm.
A. -q
B. q
Both follow from Gauss' law. Consider a spherical surface inside the metal between the interior and exterior surface (for A.). There can be no E-field flux through that surface, so the total charge inside must be zero.
Outside the sphere (for B.), the net flux is due to the charge at the center, because the surface charges on the inside and exterior of the sphere cancel.
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