Mastering Physics: The Charge Inside a Conductor

Mastering Physics: 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.

Figure 1

Part A

Question: What is the total surface charge q_int on the interior surface of the conductor (i.e., on the wall of the cavity)?

Answer: q_int =  −q

Part B

Question: What is the total surface charge q_ext on the exterior surface of the conductor?

Answer: q_ext =  q

Part C

Question: What is the magnitude E_int of the electric field inside the cavity as a function of the distance r from the point charge? Let k, as usual, denote 1/(4πϵ_0).

Answer: kq/r^2

Part D

Question: What is the electric field E_ext outside the conductor?

Answer: the same as the field produced by a point charge q located at the center of the sphere

Part E

Question: The total surface charge on the wall of the cavity, q_int:

Answer: would not change

Part F

Question: The total surface charge on the exterior of the conductor, q_ext:

Answer: would not change

Part G

Question: The electric field within the cavity, E_cav:

Answer: would not change

Part H

Question: The electric field outside the conductor, E_ext:

Answer: would change