A point charge +Q is placed inside a conducting slab. Choose the correct statements:
(A) The induced charge on the inner surface of the slab is -Q.
(B) The electric field inside the conducting slab is zero
(C) The total induced charge on the outer surface of the conducting slab is +Q
(D) The electric potential inside the slab is zero.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (B) and (C) only
In electrostatic equilibrium the electric field inside the material of a conductor is zero. The charge +Q sits in a cavity inside the slab, which is taken as initially uncharged.
A Gaussian surface drawn in the conducting material round the cavity has zero field on it, so it encloses zero charge:
\( +Q + q_{\mathrm{inner}} = 0 \)
\( q_{\mathrm{inner}} = -Q \)
(A) The induced charge on the inner surface of the slab is -Q. — Correct. This follows from Gauss’s law as shown above.
(B) The electric field inside the conducting slab is zero — Correct. The free electrons rearrange until the field in the conducting material vanishes.
(C) The total induced charge on the outer surface of the conducting slab is +Q — Correct. By conservation of charge, the uncharged slab with −Q on its inner surface carries +Q on its outer surface.
(D) The electric potential inside the slab is zero. — Incorrect. Zero field makes the whole slab an equipotential, but that potential is not zero, because of the charge +Q on the outer surface.