Question

the charge inside a conductor
(figure 1) 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.
part b
what is the total surface charge ( q_{\text{ext}} ) on the exterior surface of the conductor?
( q_{\text{ext}} = ) text box
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part c
what is the magnitude ( e_{\text{int}} ) of the electric field inside the cavity as a function of the distance ( r ) from the point charge? let ( k ), as usual, denote ( \frac{1}{4piepsilon_0} ).
options: 0, ( \frac{kq}{r^2} ), ( \frac{2kq}{r^2} )
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Explanation:

Part B

Step1: Recall conductor charge behavior

In a neutral conductor, when a charge \( +q \) is inside the cavity, the inner surface of the cavity induces \( -q \). Since the conductor is neutral initially, the exterior surface must have charge \( +q \) to maintain neutrality (total charge on conductor: inner (\( -q \)) + outer (\( q_{\text{ext}} \)) = 0 ⇒ \( q_{\text{ext}} = q \)).

Step1: Apply Gauss's Law

The cavity is inside a conductor, but the electric field inside the cavity (not in the conductor material) is due to the point charge \( +q \). Gauss's Law for a point charge: \( E = \frac{kq}{r^2} \) (where \( k=\frac{1}{4\pi\epsilon_0} \)), as the conductor's induced charges on the cavity wall don't affect the field inside the cavity (they cancel outside the cavity region for the interior field).

Answer:

\( q \)

Part C