A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge, of positive charge q. (picture attached)
a)What is the total surface charge q(int) on the interior surface of the conductor (i.e., on the wall of the cavity)?
Gauss's Law: ∫= closed surface integral-
The Attempt at a Solution
a) Since the conductor is neutral this means it has just as many electrons as protons, however since it is a conductor the electrons are loosely bound and can move. These loosely bound electrons will migrate toward the outer edge of the hollowed portion of the sphere leaving an excess charge of -q on it. My intuition tells me this is correct, but how would I go about solving/proving this with gauss's law? is gauss's Law necessary?
If I used Gauss's Law would I draw my gaussian surface like (figure 1 attached)?
With the way I drew It I wouldn't know my radius.
So my next thought was to draw it with the same radius as the hollowed out portion, lets call it "r"
But what would my Q enclosed be? clearly I am only enclosing a (+)q. This is where I am stuck.
I know the answer is -q but cannot prove/explain/show why.