Question
(a) A conductor A with a cavity as shown in figure (a) is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor.
(b) Another conductor B with charge q is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is Q + q [Fig. (b)].
(c) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.
Solution
(a) Let us take a Gaussian surface which is lying completely within the conductor and enclosing the cavity. According to the Gaussian theorem, the charge enclosed by Gaussian surface must be zero as electric field vanishes everywhere inside a conductor. Thus, electric field vanishes inside the cavity. Therefore, charges which are supplied to the conductor reside on its outer surface.
(b) Let us take a Gaussian surface inside the conductor which is quite close to the cavity. According to the Gaussian theorem,
As the electric field inside the conductor is zero,
the total charge which is enclosed by the gaussian surface must be zero. This requires, a charge of –q units to be induced on the inner surface of the hollow conductor A. But an equal and opposite charge +q units must appear on the outer surface of conductor A, so that the total charge on the outer surface of A is Q + q.
(c) Use a metallic surface to enclose the sensitive instrument completely safe and intact. Because of electrostatic shielding, the electric field inside the metal surface vanishes to zero and all charge will reside on outer surface.
(b) Let us take a Gaussian surface inside the conductor which is quite close to the cavity. According to the Gaussian theorem,
As the electric field inside the conductor is zero,
the total charge which is enclosed by the gaussian surface must be zero. This requires, a charge of –q units to be induced on the inner surface of the hollow conductor A. But an equal and opposite charge +q units must appear on the outer surface of conductor A, so that the total charge on the outer surface of A is Q + q.
(c) Use a metallic surface to enclose the sensitive instrument completely safe and intact. Because of electrostatic shielding, the electric field inside the metal surface vanishes to zero and all charge will reside on outer surface.
