Final answer:
A point charge q placed at the center of a conducting shell results in a zero electric field and electric potential inside the shell, a charge of +q on the inner surface of the shell, and zero charge on the outer surface of the shell.
Step-by-step explanation:
In the given scenario, a point charge q is placed at the center of a spherical conducting shell. Let's address each statement one by one:
A) The electric field inside the shell is zero.
This statement is correct. According to Gauss's Law, the electric field inside a conductor is zero. Therefore, the electric field inside the conducting shell is zero.
B) The electric potential inside the shell is zero.
This statement is also correct. Inside a conductor, the electric potential is constant and the same throughout the entire volume. Therefore, the electric potential inside the conducting shell is zero.
C) The charge on the inner surface of the shell is -q.
This statement is incorrect. The charge on the inner surface of the shell is equal in magnitude but opposite in sign to the charge at the center. So, it would be +q, not -q.
D) The charge on the outer surface of the shell is -q.
This statement is also incorrect. The charge on the outer surface of the conducting shell is zero. Since the electric field inside the shell is zero, the charges redistribute themselves to cancel out any electric field within the conductor. Therefore, the electric field on the outer surface of the shell is zero.