A spherical conducting shell has charge Q.A particle with charge q is placed at the center of the cavity.The charge on the inner surface of the shell and the charge on the outer surface of the shell, respectively, are:
A)0, Q
B)q, Q - q
C)Q, 0
D)-q, Q + q
E)-q, 0

Question

Quizplus · Accepted Answer

When the particle with charge q is placed at the center of the cavity, it induces a charge of -q on the inner surface of the spherical shell, due to the principle of superposition. This is because the net electric field inside the cavity due to the charges on the inner surface of the shell and the charge q is zero. Therefore, the charge on the inner surface of the shell is -q.
Now, since the spherical shell is a conductor and is in electrostatic equilibrium, the net electric field inside it must be zero. Therefore, the charge on the outer surface of the shell must be equal and opposite to the charge on the inner surface, in order to cancel the electric field inside the conductor. Therefore, the charge on the outer surface of the shell is Q + q, making the correct choice D.

A Spherical Conducting Shell Has Charge Q