# (a) A conductor A with a cavity as shown in Fig. 1.36(a) is given a charge Q.

Question:

(a) A conductor A with a cavity as shown in Fig. 1.36(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 is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is [Fig. 1.36(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 consider a Gaussian surface that is lying wholly within a conductor and enclosing the cavity. The electric field intensity E inside the charged conductor is zero.

Let q is the charge inside the conductor and is the permittivity of free space.

According to Gauss’s law,

Flux, $\phi=\vec{E} \cdot \overrightarrow{d s}=\frac{q}{\epsilon_{0}}$

Here, $E=0$

$\frac{q}{\epsilon^{0}}=0$

$\because €_{0} \neq 0$

$\therefore q=0$

Therefore, charge inside the conductor is zero.

The entire charge Q appears on the outer surface of the conductor.

(b) The outer surface of conductor A has a charge of amount Q. Another conductor B having charge +q is kept inside conductor A and it is insulated from A. Hence, a charge of amount −will be induced in the inner surface of conductor A and +q is induced on the outer surface of conductor A. Therefore, total charge on the outer surface of conductor A is Q q.

(c) A sensitive instrument can be shielded from the strong electrostatic field in its environment by enclosing it fully inside a metallic surface. A closed metallic body acts as an electrostatic shield.