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 d: what is the electric field ( e_{\text{ext}} ) outside the conductor? options: zero, the same as the field produced by a point charge q located at the center of the sphere, the same as the field produced by a point charge located at the position of the charge in the cavity. part e: now a second charge, ( q_2 ), is brought near the outside of the conductor. which of the following quantities would change? the total surface charge on the wall of the cavity, ( q_{\text{int}} ): would change, would not change.

Explanation:

Part D

In a neutral conducting sphere with a charge \( q \) at the cavity center, the inner surface of the cavity gets \( -q \) (by induction), and the outer surface gets \( +q \). Outside the conductor, the electric field is determined by the outer - surface charge, which acts like a point charge \( q \) at the center. So the external electric field \( E_{\text{ext}} \) is the same as that produced by a point charge \( q \) at the sphere's center.

The charge on the cavity wall (\( q_{\text{int}} \)) is induced by the charge \( q \) inside the cavity. The external charge \( q_2 \) does not affect the charge distribution on the cavity wall (since the electric field inside the conductor is zero, and the cavity - wall charge is determined by the internal charge \( q \)). So the total surface charge on the wall of the cavity would not change.

Answer:

the same as the field produced by a point charge \( q \) located at the center of the sphere

Part E